# How do you find the integral of #(sin^(-1)x)^2#?

Then:

Next, let's integrate by parts:

So:

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To find the integral of ((\sin^{-1}x)^2), you can use integration by parts. Let ( u = \sin^{-1}x ) and ( dv = \sin^{-1}x , dx ). Then, ( du = \frac{1}{\sqrt{1-x^2}} , dx ) and ( v = x\sin^{-1}x + \sqrt{1-x^2} ). After integrating by parts and simplifying, you'll get the integral as ( x(\sin^{-1}x)^2 - 2x\sqrt{1-x^2}\sin^{-1}x + 2x\sqrt{1-x^2} - 2x^2 + 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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