AP EAMCET2015MathematicsIndefinite Integration
e^x x^2+1 (x+1)^2 d x is equal to
Options
- Ae^x x+1 +C
- B-e^x x+1 +C
- Ce^x ( x-1 x+1 )+C
- De^x ( x+1 x-1 )+C
Correct answer
C. e^x ( x-1 x+1 )+C
Step-by-step solution
aligned & Let I= e^x x^2+1 (x+1)^2 d x= e^x ( x^2-1+2 (x+1)^2 ) d x & = e^x ( x^2-1 (x+1)^2 + 2 (x+1)^2 ) d x & = e^x ( x-1 x+1 + 2 (x+1)^2 ) d x aligned Put f(x)= x-1 x+1 aligned & f^ (x)= (x+1) d d x (x-1)-(x-1) d d x (x+1) (x+1)^2 & = (1)(x+1)-(x-1)(1) (x+1)^2 & = 2 (x+1)^2 aligned As we know, e^x f(x)+f^ (x) d x=e^x f(x)+C I=e^x ( x-1 x+1 )+C