# How do you integrate #int e^xsinx# by parts from #[0,1]#?

The answer is

The integration by parts is applied 2 times

Here,

We do the integration by parts a second time

Therefore,

So,

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To integrate (\int_0^1 e^x \sin(x) , dx) by parts, you can use the formula:

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

Let (u = \sin(x)) and (dv = e^x , dx). Then, differentiate (u) to find (du), and integrate (dv) to find (v).

After finding (u), (du), (v), and (dv), you can apply the integration by parts formula to find the integral.

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