# Hot Integral - 16

Calculus Level 5

$\textbf{Bessel Function}$ $\displaystyle \int\limits_{0}^{\infty} \log^3(x)J_n(x) dx = \left(\psi^{(a)}(\frac{n+b}{c}) + \log d\right)^f + \frac{g}{h}\psi^{(i)}\left(\frac{n+k}{l}\right)$

Find $$a+b+c+d+f+g+h+i+k+l$$

Clarifications:

• $$J_n(x)$$ is the Bessel function.

• $$\psi^{(\lambda)}(\cdot)$$ represents their usual meanings (Polygamma)

## All fractions are in their simplest form .

This is a part of Hot Integrals

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