`int ae^x dx`

Evaluate the followig integrals (i) int xe^x dx " " (ii) int x cos x dx " " (iii) int log x dx " " (iv) int sin^(-1)x dx .

int x^(x)dx

If u and v are two functions of x then prove that : int uv dx = u int v dx - int [ (du)/(dx) int v dx ] dx Hence, evaluate int x e^(x) dx

Integrate the following with respect to x. (i) int tan x dx " " (ii) int cot x dx " " (iii) int cosec x dx " " (iv) int sec x dx .

int e^x {f(x)-f'(x)}dx= phi(x) , then int e^x f(x) dx is

int e^(x log a ) e^(x) dx is equal to A) (a^(x))/( log ae) + C B) ( e^(x))/( 1+log a ) + C C) ( ae )^(x) +C D) ((ae)^(x))/( log ae) +C

"If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

"If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

"If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then