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Reverse power rule review

Review your knowledge of the reverse power rule for integrals and solve problems with it.

What is the reverse power rule?

The reverse power rule tells us how to integrate expressions of the form xn where n1:
xndx=xn+1n+1+C
Basically, you increase the power by one and then divide by the power +1.
Remember that this rule doesn't apply for n=1.
Instead of memorizing the reverse power rule, it's useful to remember that it can be quickly derived from the power rule for derivatives.
Want to learn more about the reverse power rule? Check out this video.

Integrating polynomials

We can use the reverse power rule to integrate any polynomial. Consider, for example, the integration of the monomial 3x7:
3x7dx=3(x7+17+1)+C=3(x88)+C=38x8+C
Remember you can always check your integration by differentiating your result!
Problem 1
14tdt=?
Choose 1 answer:

Want to try more problems like this? Check out these exercises:

Integrating negative powers

The reverse power rule allows us to integrate any negative power other than 1. Consider, for example, the integration of 1x2:
1x2dx=x2dx=x2+12+1+C=x11+C=1x+C
Problem 1
8t3dt=
Choose 1 answer:

Want to try more problems like this? Check out these exercises:

Integrating fractional powers and radicals

The reverse power rule also allows us to integrate expressions where x is raised to a fractional power, or radicals. Consider, for example, the integration of x:
xdx=x12dx=x12+112+1+C=x3232+C=2x33+C
Problem 1
4t13dt=?
Choose 1 answer:

Want to try more problems like this? Check out these exercises:

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