`int2^(log_e x)dx`

If a gt0 and a!=1 evaluate the following integrals: (i) int e^(xlog_(e)a)dx (ii) int e^(alog_(e)x)dx (iii) int e^x a^xdx (iv) int 2^(log_(e)x)dx

int e^(log_(e)x)dx

int (1+log_e x)/x dx

int cos (log_e x)dx is equal to

int cos (log_e x)dx is equal to

int sin^(2)(log_(e)x)dx

Evaluate int 2e^(ln x) dx .

Evalute the following integrals int e^(2 log x) dx

int e^(2log sec x)dx