# How do you find the indefinite integral of #int sin^3xcosxdxdx#?

Substituting into the integral gives:

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To find the indefinite integral of ∫sin^3(x)cos(x)dx, you can use the substitution method. Let u = sin(x), then du = cos(x)dx. Substitute these into the integral to get:

∫sin^3(x)cos(x)dx = ∫u^3 du

Now integrate with respect to u:

∫u^3 du = (1/4)u^4 + C

Replace u with sin(x):

(1/4)sin^4(x) + C

So, the indefinite integral of ∫sin^3(x)cos(x)dx is (1/4)sin^4(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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