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∫0πexx3cosx dx \large \displaystyle \int_{0}^{\pi} e^{x} x^{3} \cos x \, dx ∫0πexx3cosxdx
If the above integral can be expressed in the form −ab−ceπd+fπeπg−hπjeπk, -\dfrac{a}{b} - \dfrac{c e^{\pi}}{d} + \dfrac{f\pi e^{\pi}}{g} - \dfrac{h \pi^{j} e^{\pi}}{k}, −ba−dceπ+gfπeπ−khπjeπ, where a,b,c,d,f,g,h,ja, b, c, d, f, g, h, ja,b,c,d,f,g,h,j and k k k are positive integers with gcd(a,b)=gcd(c,d)=gcd(f,g)=gcd(h,k)=1\gcd(a, b) = \gcd(c, d) = \gcd(f, g) = \gcd (h, k) = 1 gcd(a,b)=gcd(c,d)=gcd(f,g)=gcd(h,k)=1, and e e e is Euler's number, find a+b+c+d+f+g+h+j+k a+b+c+d+f+g+h+j+ka+b+c+d+f+g+h+j+k.
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