7. `int(log sqrt(x))^(2)dx`

Evaluate the following Integrals. int x (log x)^(2) dx

Evaluate the following Integrals. int log (x^(2) +a^(2))dx

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

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

Prove that : int_(0)^(1) (log x)/(sqrt(1-x^(2)))dx=-(pi)/(2)log 2

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

STATEMENT-1 : int_(-(pi)/(2))^((pi)/(2))sin(log(x+sqrt(1+x^(2))))dx=0 and STATEMENT-2 : int_(-a)^(a)f(x)dx=0 if f(x) is an even function

int log ( 1 + x^(2)) dx

int((log _(e)x)^(3))/(x)dx

int(tan(1+log x))/(x) dx