KCET2012MathematicsIndefinite Integration
If n N and I _ n = ( x )^ n dx , then I _ n + n I _ n -1 is equal to
Options
- A( x)^ n +1 n +1
- Bx( x)^ n +C
- C( x)^ n -1
- D( x)^ n n
Correct answer
B. x( x)^ n +C
Step-by-step solution
Here, I _ n = ( x )^ n dx On initegrating by parts, we get aligned & I _ n =( x )^ n x - x n ( x )^ n -1 1 x dx & I _ n = x ( x )^ n nI _ n -1 & I _ n + nI _ n -1 = x ( x )^ n + C aligned