# How do you integrate #int xarctanx# by integration by parts method?

Thus:

Rewrite the numerator or perform polynomial long division of the integrand. Both will result in equivalent simplifications:

Both of these are simply integrated:

Or:

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To integrate ( \int x \arctan(x) ) using integration by parts:

- Choose ( u = \arctan(x) ) and ( dv = x , dx ).
- Compute ( du ) and ( v ) using the derivatives and antiderivatives of ( u ) and ( dv ).
- Apply the integration by parts formula: ( \int u , dv = uv - \int v , du ).
- Substitute the values of ( u ), ( du ), ( v ), and ( dv ) into the integration by parts formula and evaluate the resulting integral.

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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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