I want show that $\int _0^{\infty}x^{4n+3}\exp(-x)\sin(x)dx=0$ for $n\in \mathbb{N}$.
How can I prove this?Do I need to use $\sin(x)=\Im(\exp(ix))$ and complex integral?
I want to know how to prove it well.
I want show that $\int _0^{\infty}x^{4n+3}\exp(-x)\sin(x)dx=0$ for $n\in \mathbb{N}$.
How can I prove this?Do I need to use $\sin(x)=\Im(\exp(ix))$ and complex integral?
I want to know how to prove it well.