`"If " I=int e^(-x)log(e^(x)+1)dx, " then " I " equals "`

If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)+C a+(e^x+1)log(e^x+1)+C a-(e^(-x)+1)log(e^x+1)+C none of these

If I=int_(0)^(1) (1+e^(-x^2)) dx then, s

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

int (1+log_e x)/x dx

I=int(e^(x))/((e^(x)+1)^(1//4))dx is equal to

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

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

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

Statement -1 : If I_(1)=int(e^(x))/(e^(4x)+e^(2x)+1)dx and I_(2)=int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx , then I_(2)-I_(1)=(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+C where C is an arbitrary constant. Statement -2 : A primitive of f(x) =(x^(2)-1)/(x^(4)+x^(2)+1) is (1)/(2)log((x^(2)-x+1)/(x^(2)+x+1)) .

If I_(n)=int_(0)^(pi) e^(x)sin^(n)x " dx then " (I_(3))/(I_(1)) is equal to