# What is the antiderivative of #x^2(sinx)dx#?

Make two uses of integration by parts.

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The antiderivative of ( x^2 \sin(x) ) with respect to ( x ) is ( -x^2 \cos(x) + 2x \sin(x) + 2 \cos(x) + C ), where ( C ) is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- What is the integral from 0 to 16 of #1/(16-x) dx#?
- How do you integrate #int x^3*dx/(x^2-1)^(2/3)#?

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