" (i) grafe "(8,5,int_(0)^(log_(6)(1+x))dx=pi/8log_(e)^(2)

int_(1)^(x)log_(e)[x]dx

int_(0)^(pi)log(1+cosx)dx=-pi(log2)

int_(0)^(1)(log|1+x|)/(1+x^(2))dx=(pi)/(8)log2

Show that int_0^1(log(1+x))/(1+x^2)dx=pi/8log2

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

" 8."int_(0)^(oo)(log x)/(1+x^(2))dx

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

int_(0)^(2pi) ln (1+Cos x) dx=

8. int_0^(pi/4) log(1+tanx)dx