MHT CET2012MathematicsIndefinite Integration
The value of d x x (x^ n +1 ) is
Options
- A1 n ( x^ n x^ n +1 )+C
- B( x^ n +1 x^ n )+C
- C1 n ( x^ n +1 x^ n )+C
- D( x^ n x^ n +1 )+C
Correct answer
A. 1 n ( x^ n x^ n +1 )+C
Step-by-step solution
Let aligned I= d x x (x^ n +1 ) . (let t=x^ n +1, d t=n x^ n-1 d x ) =& d t r x^ n t ( d t n x^ n = d x x ) =& 1 n d t t(t-1) =& 1 n 1 t-1 - 1 t d t =& 1 n (t-1)- t +C =& 1 n t-1 t +C =& 1 n x^ n x^ n +1 +C aligned