# How do you find the antiderivative of #int (arctan(sqrtx)) dx#?

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To find the antiderivative of (\int \arctan(\sqrt{x}) , dx), use integration by parts with (u = \arctan(\sqrt{x})) and (dv = dx). Differentiate (u) and integrate (dv) to find (du) and (v). Then apply the integration by parts formula:

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

Finally, substitute the expressions for (u), (v), (du), and integrate the resulting expression.

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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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