# How do you find the integral of #(sin^3(x/2))(cos(x/2))#?

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To find the integral of ( \sin^3(\frac{x}{2}) \cdot \cos(\frac{x}{2}) ), you can use the substitution method. Let ( u = \sin(\frac{x}{2}) ), then ( du = \frac{1}{2} \cos(\frac{x}{2}) dx ). Rewrite the integral in terms of ( u ) and ( du ), and it becomes ( 2\int u^3 du ). Now, integrate ( u^3 ) with respect to ( u ), then replace ( u ) with ( \sin(\frac{x}{2}) ) to get the final result.

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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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