AP EAMCET2015MathematicsIndefinite Integration
d x (x-1) x^2-1 is equal to
Options
- A- x-1 x+1 +C
- Bx-1 x^2+1 +C
- C- x+1 x-1 +C
- Dx^2+1 x-1 +C
Correct answer
C. - x+1 x-1 +C
Step-by-step solution
Let I= d x (x-1) x^2-1 Put x-1= 1 t x=1+ 1 t Then, d x= -1 t^2 d t aligned & I= - 1 t^2 d t 1 t (1+ 1 t )^2-1 =- d t t 1+ 1 t^2 + 2 t -1 & =- d t t 1+2 t t^2 =- d t 1+2 t & =- (1+2 t)^ - 1 2 d t & =- (1+2 t)^ - 1 2 +1 - 1 2 +1 1 2 & =- 1+2 t +C & =- 1+2 ( 1 x-1 ) +C=- x-1+2 x-1 +C aligned Thus, I=- x+1 x-1 +C