## integrate

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Indefinite Integral - Basic Integration Rules, Problems, Formulas, Trig Functions, Calculus

This calculus video tutorial explains how to find the indefinite integral of function. It explains how to apply basic integration rules and formulas to help you integrate functions. This video contains plenty of examples and practice problems.

Calculus Textbooks:

https://amzn.to/3cfUeTS

My Website: https://www.video-tutor.net

Calculus Video Playlist:

https://www.youtube.com/watch?v=rCxi-O79sVo\u0026t=25s\u0026index=1\u0026list=PL0o_zxa4K1BVKErFko9je9IBZ0hXWXVtV

Access to Premium Videos:

https://www.patreon.com/MathScienceTutor

Here is a list of topics:

1. Basic Integration Rules and Formulas

2. Indefinite Integral and Constant of Integration

3. Integrating Constants and Linear Functions

4. Parabolic and Quadratic Functions

5. Polynomial Functions

6. Integration of Rational Functions and Fractions

7. Indefinite Integral - Square Root and Radical Functions

8. Exponential Functions and Natural Logarithms

9. Trig Functions, Sine, Cosine, Tangent, and Secant

10. Integration Techniques - U-Substitution, Integration By Parts, and Trigonometric Substitution.

Basic Integration... How? (NancyPi)

MIT grad shows how to find antiderivatives, or indefinite integrals, using basic integration rules. To skip ahead: 1) For how to integrate a polynomial with the POWER RULE, skip to 1:35. 2) For how to integrate NEGATIVE POWERS of x, FRACTIONAL POWERS of x, and RADICALS/ROOTS, skip to 6:12. 3) For how to integrate x^(-1), or 1/x, with the LOG RULE, skip to 7:23. 4) For examples where you use more algebra to rewrite before integrating, to SEPARATE the numerator of a FRACTION, or EXPAND a PRODUCT in order to use the Power Rule, skip to 10:00. 5) For basic TRIG and EXPONENTIAL examples that use rules from the Table of Integrals, as well as trig identities, skip to 11:36. Nancy formerly of MathBFF explains the steps.

For my video on how to integrate using U-SUBSTITUTION, jump to:

For my video on how to do INTEGRATION BY PARTS, jump to:

Follow Nancy on Instagram: https://instagram.com/nancypi

Twitter: https://twitter.com/nancypi

1) POWER RULE: If you're integrating a polynomial, or just a power of x, you can use the Power Rule on each x-term in the polynomial. The Power Rule says that for a term that's just a power of x, such as x^3, you can integrate by raising the power by 1 AND dividing by that number (the new number you got by increasing the power by 1). For example, the integral of x^3 would be (x^4)/4. If there was a constant multiplied in front of the x-power, you can keep the constant and integrate the rest of the term (Constant Multiple Rule). For example, the integral of 6x^2 would be 6 times (x^3)/3, which simplifies to 2x^3. You can repeat these steps to integrate every term in the polynomial and string them together for the full integral. You can also keep the addition and subtraction between the terms (because of the Sum and Difference Rules). NOTE: The anti-derivative of a constant (just a number) is always that number times x (the Constant Rule), so the integral of 1 is 1*x, or x. At the end, it's very important to remember to add a constant of integration, to include a "+ c" at the end of your answer, when it is an indefinite integral (integral with no limits). ANOTHER NOTE: The Power Rule only works when the power is not -1.

2) NEGATIVE \u0026 FRACTIONAL POWERS, and RADICALS: For negative powers, you can still use the Power Rule, as long as the power is not -1. For fractional powers, you can also use the Power Rule. When you increase a fractional power by 1, you will have to simplify the power (before integrating) by getting a common denominator. For roots, like the square root of x, it's best to rewrite the radical as a fractional power, and then use the Power Rule.

3) IF THE X POWER IS -1 in the integrand, either written as x^(-1) or 1/x, you have to use a special rule, the LOG RULE, that you can find on a Table of Integrals. It says that the anti-derivative of x^(-1), or (1/x) is the natural log of the absolute value of x, plus c.

4) MORE ALGEBRA: Sometimes you may need to do a bit more algebra before integrating, so that the integrand is in a form that fits a basic integration rule, like the Power Rule. If you're integrating a rational expression, you can sometimes separate the numerator, or break the fraction into separate fractions, simplify each term, and then integrate with the Power Rule. If you have a product of x expressions, you can multiply it out, or distribute the factors so that you have just a polynomial (and can use the Power Rule).

5) TRIG \u0026 EXPONENTIAL: You can find a lot of trigonometric (and exponential) integral rules in the Table of Integrals. If you don't see it in the table, you may need to use a trig identity first, to rewrite the integrand into a form that you can integrate.

For more of my math videos, check out: http://nancypi.com

Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems

This calculus video tutorial explains how to calculate the definite integral of function. It provides a basic introduction into the concept of integration. It provides plenty of examples and practice problems for you to work on.

Calculus Textbooks:

https://amzn.to/3cfUeTS

My Website: https://www.video-tutor.net

Patreon: https://www.patreon.com/MathScienceTutor

Calculus Video Playlist:

https://www.youtube.com/watch?v=rCxi-O79sVo\u0026t=25s\u0026index=1\u0026list=PL0o_zxa4K1BVKErFko9je9IBZ0hXWXVtV

Here is a list of topics:

1. Basic Integration Rules Explained

2. Finding the Definite Integral

3. Definite Integral of Constants and Linear Functions

4. Polynomial Functions

5. Square Root Functions and Radicals

6. Integration of Exponential Functions - e

7. Rational Functions and Fractions

8. Natural Logarithms

9. Definite Integral of Trig Functions - sin x and cos x

10. U-substitution \u0026 definite integrals

11. Integration by parts

This calculus video tutorial explains how to find the indefinite integral of function. It explains how to apply basic integration rules and formulas to help you integrate functions. This video contains plenty of examples and practice problems.

Calculus Textbooks:

https://amzn.to/3cfUeTS

My Website: https://www.video-tutor.net

Calculus Video Playlist:

https://www.youtube.com/watch?v=rCxi-O79sVo\u0026t=25s\u0026index=1\u0026list=PL0o_zxa4K1BVKErFko9je9IBZ0hXWXVtV

Access to Premium Videos:

https://www.patreon.com/MathScienceTutor

Here is a list of topics:

1. Basic Integration Rules and Formulas

2. Indefinite Integral and Constant of Integration

3. Integrating Constants and Linear Functions

4. Parabolic and Quadratic Functions

5. Polynomial Functions

6. Integration of Rational Functions and Fractions

7. Indefinite Integral - Square Root and Radical Functions

8. Exponential Functions and Natural Logarithms

9. Trig Functions, Sine, Cosine, Tangent, and Secant

10. Integration Techniques - U-Substitution, Integration By Parts, and Trigonometric Substitution.

Basic Integration... How? (NancyPi)

MIT grad shows how to find antiderivatives, or indefinite integrals, using basic integration rules. To skip ahead: 1) For how to integrate a polynomial with the POWER RULE, skip to 1:35. 2) For how to integrate NEGATIVE POWERS of x, FRACTIONAL POWERS of x, and RADICALS/ROOTS, skip to 6:12. 3) For how to integrate x^(-1), or 1/x, with the LOG RULE, skip to 7:23. 4) For examples where you use more algebra to rewrite before integrating, to SEPARATE the numerator of a FRACTION, or EXPAND a PRODUCT in order to use the Power Rule, skip to 10:00. 5) For basic TRIG and EXPONENTIAL examples that use rules from the Table of Integrals, as well as trig identities, skip to 11:36. Nancy formerly of MathBFF explains the steps.

For my video on how to integrate using U-SUBSTITUTION, jump to:

For my video on how to do INTEGRATION BY PARTS, jump to:

Follow Nancy on Instagram: https://instagram.com/nancypi

Twitter: https://twitter.com/nancypi

1) POWER RULE: If you're integrating a polynomial, or just a power of x, you can use the Power Rule on each x-term in the polynomial. The Power Rule says that for a term that's just a power of x, such as x^3, you can integrate by raising the power by 1 AND dividing by that number (the new number you got by increasing the power by 1). For example, the integral of x^3 would be (x^4)/4. If there was a constant multiplied in front of the x-power, you can keep the constant and integrate the rest of the term (Constant Multiple Rule). For example, the integral of 6x^2 would be 6 times (x^3)/3, which simplifies to 2x^3. You can repeat these steps to integrate every term in the polynomial and string them together for the full integral. You can also keep the addition and subtraction between the terms (because of the Sum and Difference Rules). NOTE: The anti-derivative of a constant (just a number) is always that number times x (the Constant Rule), so the integral of 1 is 1*x, or x. At the end, it's very important to remember to add a constant of integration, to include a "+ c" at the end of your answer, when it is an indefinite integral (integral with no limits). ANOTHER NOTE: The Power Rule only works when the power is not -1.

2) NEGATIVE \u0026 FRACTIONAL POWERS, and RADICALS: For negative powers, you can still use the Power Rule, as long as the power is not -1. For fractional powers, you can also use the Power Rule. When you increase a fractional power by 1, you will have to simplify the power (before integrating) by getting a common denominator. For roots, like the square root of x, it's best to rewrite the radical as a fractional power, and then use the Power Rule.

3) IF THE X POWER IS -1 in the integrand, either written as x^(-1) or 1/x, you have to use a special rule, the LOG RULE, that you can find on a Table of Integrals. It says that the anti-derivative of x^(-1), or (1/x) is the natural log of the absolute value of x, plus c.

4) MORE ALGEBRA: Sometimes you may need to do a bit more algebra before integrating, so that the integrand is in a form that fits a basic integration rule, like the Power Rule. If you're integrating a rational expression, you can sometimes separate the numerator, or break the fraction into separate fractions, simplify each term, and then integrate with the Power Rule. If you have a product of x expressions, you can multiply it out, or distribute the factors so that you have just a polynomial (and can use the Power Rule).

5) TRIG \u0026 EXPONENTIAL: You can find a lot of trigonometric (and exponential) integral rules in the Table of Integrals. If you don't see it in the table, you may need to use a trig identity first, to rewrite the integrand into a form that you can integrate.

For more of my math videos, check out: http://nancypi.com

Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems

This calculus video tutorial explains how to calculate the definite integral of function. It provides a basic introduction into the concept of integration. It provides plenty of examples and practice problems for you to work on.

Calculus Textbooks:

https://amzn.to/3cfUeTS

My Website: https://www.video-tutor.net

Patreon: https://www.patreon.com/MathScienceTutor

Calculus Video Playlist:

https://www.youtube.com/watch?v=rCxi-O79sVo\u0026t=25s\u0026index=1\u0026list=PL0o_zxa4K1BVKErFko9je9IBZ0hXWXVtV

Here is a list of topics:

1. Basic Integration Rules Explained

2. Finding the Definite Integral

3. Definite Integral of Constants and Linear Functions

4. Polynomial Functions

5. Square Root Functions and Radicals

6. Integration of Exponential Functions - e

7. Rational Functions and Fractions

8. Natural Logarithms

9. Definite Integral of Trig Functions - sin x and cos x

10. U-substitution \u0026 definite integrals

11. Integration by parts

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