# What is the integral of #sin^5 (x) * cos^3 (x)#?

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To find the integral of sin^5(x) * cos^3(x), you can use the substitution method. Let u = sin(x), then du = cos(x) dx. Rewrite the integral in terms of u:

∫sin^5(x) * cos^3(x) dx = ∫u^5 * (1 - u^2) du.

Now, expand and integrate:

= ∫(u^5 - u^7) du = (1/6)u^6 - (1/8)u^8 + C.

Replace u with sin(x) to get the final answer:

= (1/6)sin^6(x) - (1/8)sin^8(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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