If `a >0` and `a!=1` evaluate the following integrals: `inte^(x\ (log)_e a)\ dx\ ` (ii) `inte^(a\ (log)_e x)\ dx`

If a >0 and a!=1 evaluate the following integrals: (i) inte^(x\ (log)_e a)\ dx\ (ii) inte^(a\ (log)_e x)\ dx

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

Evaluate the following integrals: int e^(x) (cotx+log sinx)dx

Evaluate the following integrals: int(x^(2) +1) log x dx

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

If a >0 and a!=1 evaluate the following integrals: inte^x\ a^x\ dx (ii) 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

If a>0 and a!=1 evaluate the following integrals: int e^(x)a^(x)dx (ii) int2^((log)_(e)x)dx

Evaluate the following integral: int_(0)^(1)log(1+x)dx