# How do you find the antiderivative of #int sinx(cosx)^(3/2) dx#?

So, we need to modify our integral just a little:

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To find the antiderivative of ∫sin(x)(cos(x))^(3/2) dx, you can use the substitution method. Let u = cos(x), then du = -sin(x) dx. Substitute these into the integral:

∫sin(x)(cos(x))^(3/2) dx = ∫-u^(3/2) du

Now integrate -u^(3/2) with respect to u:

= -(2/5)u^(5/2) + C

Substitute back u = cos(x):

= -(2/5)cos^(5/2)(x) + C

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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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