If `int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1)+B F(x-4)+C` and `F(x)=int(e^x)/xdx ,t h e n`

int(e^x+1)^2e^xdx

If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(x) is equal to

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)) .

int(x+1)/(x(1+x e^x)^2)dx=log|1-f(x)|+f(x)+c , then f(x)=

If int((x-1)/(x^2))e^x dx=f(x)e^x+c , then write the value of f(x) .

If intsin^(-1)xcos^(-1)xdx=f^(-1)(x) [π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2x+C ,t h e n f(x)=sinx (b) f(x)=cosx A=pi/4 (d) A=pi/2

int((x+2)/(x+4))^2 e^xdx is equal to

int_0^1 x^2e^xdx

If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C , then

int(cot^(-1)(e^x))/e^xdx is equal to