AP EAMCET2015MathematicsIndefinite Integration
x+1 x (1+x e^x ) d x is equal to
Options
- A| 1+x e^x x e^x |+C
- B| x e^x 1+x e^x |+C
- C|x e^x (1+x e^x ) |+C
- D|1+x e^x |+C
Correct answer
B. | x e^x 1+x e^x |+C
Step-by-step solution
aligned & Let I= x+1 x (1+x e^x ) d x & Put x e^x=t & (x e^x+e^x ) d x=d t & e^x(x+1) d x=d t & (x+1) d x= d t e^x & I= d t x e^x (1+x e^x ) = 1 t(1+t) d t= t+1-t t(t+1) d t & I= ( 1 t - 1 t+1 ) d t & = t- (t+1)+C & = | t t+1 |+C aligned Now, Substitute the value of t , we get = | x e^x x e^x+1 |+C