# How do you find the integral of #(x)(secˉ¹(x)) dx #?

Integrate by parts, making the following selections:

Then, apply the Integration by Parts formula:

Thus, we have

So, our integral is

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To find the integral of ( x \cdot \sec^{-1}(x) ) with respect to ( x ), you can use integration by parts. Let ( u = \sec^{-1}(x) ) and ( dv = x , dx ). Then, differentiate ( u ) and integrate ( dv ) to find ( du ) and ( v ). Finally, apply the integration by parts formula, which states:

[ \int u , dv = uv - \int v , du ]

Once you have computed ( uv ) and ( \int v , du ), you will have the integral of ( x \cdot \sec^{-1}(x) ).

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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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