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Exercise

∫−xncos⁡(x) +n ∫(xn−1)cos⁡(x)dx\int-x^n\cos\left(x\right)\:+n\:\int\left(x^{n-1}\right)\cos\left(x\right)dx

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Final answer to the exercise

∑n=0∞(−1)(n+1)x(3n+1)(3n+1)(2n)!+n∑n=0∞(−1)nx(3n+1)3n(3n+1)(2n)!+C0\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^{\left(n+1\right)}x^{\left(3n+1\right)}}{\left(3n+1\right)\left(2n\right)!}+n\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(3n+1\right)}}{3n\left(3n+1\right)\left(2n\right)!}+C_0

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∫−xncos(x) +n ∫(xn−1)cos(x)dx
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