# How do you evaluate the integral #int x^-2arcsinx#?

Use integration by parts. Let:

Then:

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Then perform integration by parts. Let:

So:

Which is a common integral:

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To evaluate the integral ∫ x^(-2)arcsin(x) dx, use integration by parts. Let u = arcsin(x) and dv = x^(-2) dx. Then differentiate u to find du and integrate dv to find v. After finding du and v, apply the integration by parts formula:

∫ u dv = uv - ∫ v du

Substitute the values of u, dv, du, and v into the formula and perform the integration. Then simplify the resulting expression to obtain the final answer.

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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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