`int xlog(1+x) dx`

Evaluate: int_(0)^(pi) xlog (sin x) dx

Evaluate : int_0^1xlog(1+2x)dx

Evaluate : int_0^1xlog(1+2x)dx

Evaluate : int_0^1xlog(1+2x)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

Evaluate: (i) int(e^x+1)/(e^x+x)\ dx (ii) int1/(xlogx)\ dx

int cot^-1 x dx

Evaluate: int1/(xlog_ex)dx

int (1+x)^4 dx

int sec^(-1)x dx