I don't get those integrals

Please show me how do I solve these. I need the way.
(e^(1/x))/x  dx

cos(x) * 2^(sin x)   dx

(tan(5x))^5  dx

(sin(x/2))^3  *  (cos(x/2))^5   dx

(cos(3x))^4  dx

Thanks ahead and good night.

Second looks like it might be a simple reverse chain rule. See what happens if you differentiate 2^(sinx)