# Too many parts! (My fourteenth integral problem)

Calculus Level 5

$\large \displaystyle \int_{0}^{\pi} e^{x} x^{3} \cos x \, dx$

If the above integral can be expressed in the form $-\dfrac{a}{b} - \dfrac{c e^{\pi}}{d} + \dfrac{f\pi e^{\pi}}{g} - \dfrac{h \pi^{j} e^{\pi}}{k},$ where $$a, b, c, d, f, g, h, j$$ and $$k$$ are positive integers with $$\gcd(a, b) = \gcd(c, d) = \gcd(f, g) = \gcd (h, k) = 1$$, and $$e$$ is Euler's number, find $$a+b+c+d+f+g+h+j+k$$.

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