Integrate the function $-5e^{-5t}e^{\left(t-7\right)}\cos\left(20\pi t\right)$ from 0 to $7$

Find the integral

$\int e^{3t}\sin\left(2t\right)dt$

Find the integral

$\int e^{x}\cos xdx$

Find the integral

$\int\:e^x\cos\left(x\right)dx$

Find the integral

$\int e^{3x}\cdot\cos\left(4x\right)dx$

Find the integral

$\int e^xcos2xdx$

Find the integral

$\int e^x\cdot\cos\left(x\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(xe^{-x}\right)dx$