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

We must compute:

Presently, Our integral becomes

We are going to use Integration by Parts now.

Thus, From (i),

Now,

So,

Consequently, The Complete Integration (From (iii)),

I hope this is helpful.

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The antiderivative of ( x \cdot (\sin x)^2 ) with respect to ( x ) is:

[ -\frac{1}{2} x \cos x + \frac{1}{4} \sin(2x) + 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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