`int log_(e)(a^(x))dx=`

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

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

Evaluate int 5^(log _(e)x)dx

int (1+log_e x)/x dx

Evaluate int 2^(log_(4)x)dx

The value of the integral underset(e^(-1))overset(e^(2))int |(log_(e)x)/(x)|dx is

Given overset(2)underset(1)inte^(x^(2))dx=a , the value of overset(e^(4))underset(e )int sqrt(log_(e )x)dx , is

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 : int(log_(e)(1+sin^(2)x))/(cos^(2)x)dx

If intx log (1+(1)/(x))dx =f(x).log_(e)(x+1)+g(x)log_(e)x+Lx+C , then