`int (dx)/(x^(2)-2x+2)= f(x)+c rArr f(x)=`

If int(1)/(x^(2)+2x+2)dx=f (x) +C , then f (x)=

Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int e^(x)((x-1)/(x^(2)))dx = __________.

int(f'(x))/(f(x))dx=log f(x)+c

If int(dx)/(x^(2)+ax+1)=f(g(x))+c, then

int(f'(x))/([f(x)]^(2))dx=

Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int(x e^(x))/((1+x)^(2))dx = ________.

If inte^(x)((1-x)/(1+x^(2)))^(2)dx=e^(x)f(x)+c, then f(x)=

If inte^(x)(1+x^(2))/((1+x)^(2))dx=e^(x)f(x)+c , then f(x)=