NDA2019MathematicsIndefinite IntegrationActual
What is d x x(1+ x)^n equal to (n^1 1 ) ?
Options
- A1 (n-1)(1+ x)^ n+1 +c
- B1-n (1+ x)^ n-1 +c
- Cn+1 (1+ x)^ n-1 +c
- D1 (n-1)(1+ n x)^ n-1 +c
Correct answer
D. 1 (n-1)(1+ n x)^ n-1 +c
Step-by-step solution
aligned & d x x(1+ n x)^n & Let 1+ n x=t & 1 x d x=d t & d t t^n = t^ -n +1 -n+1 aligned aligned & = (1+ n x)^ -n+1 1-n & = 1 (n-1)(1+ n x)^ n-1 +C aligned