# Would IBP work?

Calculus Level 5

Evaluate: $\int_0^{\infty} \frac{x^3\ln^2 x}{1+x^6}\,dx$

If the result can be expressed as $$\displaystyle \frac{a\pi^b}{c\sqrt{d}}$$, where $$a$$ and $$c$$ are coprime, $$b$$ is an integer and $$d$$ is a prime number, then find $$a+b+c+d$$.

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