AP EAMCET2005MathematicsIndefinite Integration
If x x(1+ x) d x=f(x)+c , then f(x) is equal to
Options
- A| 1+ x x |
- B| x 1+ x |
- C| x 1+ x |
- D| 1+ x x |
Correct answer
A. | 1+ x x |
Step-by-step solution
Let I= x x(1+ x) d x Put x=t - x d x=d t aligned I & = -d t t(1+t) & =- [ 1 t - 1 (1+t) ] d t & =-[ t- (1+t)]+c & = ( t+1 t )+c aligned aligned & But I= (x)+c & ( x+1 x )+c=f(x)+c & f(x)= ( 1+ x x ) aligned