`int((1+(log)_e x)^2)/(1+(log)_e x^(x+1)+((log)_e x^(sqrt(x)))^2)dx=`

int(e^(log sqrt(x)))/(x)dx=

int(e^(log sqrt(x)))/(x)dx

Evaluate: int(e^(5\ (log)_e x)-e^(4\ (log)_e x))/(e^(3\ (log)_e x)-e^(2\ (log)_e x))\ dx

int_(1)^(e^(2))(ln x)/(sqrt(x))dx=

Evaluate: int(e^(5)(log)_(e)x-e^(4)(log)_(e)x)/(e^(3)(log)_(e)x-e^(2)(log)_(e^(x))x)dx

int_(1)^(e )(1)/(x sqrt(log x))dx=

int(e^(ln x))/(1+x^(2))dx

-int_(1)^(e)((log x)^(2))/(x)*dx

If y=tan^(-1){((log)_e(e//x^2))/((log)_e(e x^2))}+tan^(-1)((3+2\ (log)_e x)/(1-6\ (log)_e x)) , then (d^2y)/(dx^2)= (a) 2 (b) 1 (c) 0 (d) -1

int(e^(x log a)+e^(a log x)+e^(a log a))dx