`int e^x(x+lnx) (x+1) dx`

int e^(x)/(e^(x)+1) dx =

int x^(x^2+1) (2lnx+1) dx=

What is int e^(lnx) sin x dx equal to ? Where 'c' is a constant of integration

(i) int (dx)/(e^x+e^(-x)) (ii) int e^x/(e^(2x)+1) dx

int (e^(x))/(1+e^(x))dx

(i) int (e^x dx)/(e^x (e^x-1)) (ii) int e^x/((1+e^x)(2+e^x)) dx (iii) int e^x/((e^x-1)^2(e^x+2)) dx

Show that int x ^(n) . e ^(-x) dx= -x^(n) e ^(-x) +n int x ^(n-1) . e ^(-x) dx

Evaluate: (i) int e^(x)((1)/(x)-(1)/(x^(2)))dx (ii) int e^(x)(sin x+cos x)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 = ________.

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 = __________.