Manipal MET2013MathematicsIndefinite Integration
If Th x^2 (x^n+1 )^ 1-1) n :=-[f(x)]^ 1 / n +c then f(x) is
Options
- A1+x^n
- B1+x^ -n
- Cx^n+x^ -n
- DNone of these
Correct answer
B. 1+x^ -n
Step-by-step solution
We have; d x x^2 (x^n+1 )^ (n-1) n = d x x^2 x^ n-1 (1+ 1 x^n )^ (n-1) n = d x x^ n+1 (1+x^ -n )^ (n-1) n Put, 1+x^ -n =t -n x^ -n-1 d x=d t d x x^ n+1 = -d t n d x x^2 (x^n+1 )^ (n-1) n =- 1 n d t t^ (n-1) n =- 1 n t^ (1 / n)-1 d t=- 1 n t^ ( 1 n -1+1 ) ( 1 n -1+1 ) +c=-t^ 1 / n +c=- (1+x^ -n )^ 1 n +c