KCET2026MathematicsIndefinite Integration
If ' n ' is a natural number, then ^n x ^ n+2 x ,dx =
Options
- A^ n-1 x n - 1 + C
- B^n x n + C
- C^ n+2 x n + 2 + C
- D^ n+1 x n + 1 + C
Correct answer
D. ^ n+1 x n + 1 + C
Step-by-step solution
The given integral is I = ^n x ^ n+2 x ,dx This can be rewritten as: I = ( x x )^n 1 ^2 x ,dx I = ^n x ^2 x ,dx Let x = t , then ^2 x ,dx = dt Substituting these into the integral, we get: I = t^n ,dt I = t^ n+1 n+1 + C I = ^ n+1 x n+1 + C Answer: ^ n+1 x n + 1 + C