Solve the integral of logarithmic functions $\int\sin\left(\ln\left(x\right)\right)dx$

Find the integral

$\int sin\left(\ln\left(x\right)\right)dx$

Find the integral

$\int e^{2x}cosxdx$

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

$\int e^xcos2xdx$