This is a hard integral.

If you call then thus you need an .

You split is as,

Use substitution rule,

Now, you need to do integration by parts.

Let and .

Thus, and .

Integration by parts,

Substitute back (and multiply by 1/3 from beginning),

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If you want a website to check your integration work,

You can use The Integrator--Integrals from Mathematica