NDA2020MathematicsIndefinite IntegrationActual
What is d x x (x^n+1 ) equal to?
Options
- A1 n ( x^n x^n+1 )+c
- B( x^n+1 x^n )+c
- C( x^n x^n+1 )+c
- D1 n ( x^n+1 x^n )+c
Correct answer
A. 1 n ( x^n x^n+1 )+c
Step-by-step solution
d x x (x^n+1 ) = x^ n-1 x^n (x^n+1 ) d x Let z=x^n d z=n x^ n-1 d x d x x (x^n+1 ) = x^ n-1 x^n (x^n+1 ) d x= 1 z(z+1) d z n aligned & = 1 n [ 1 z d z- d z z+1 ] & = 1 n [ z- (z+1)]+C where C= constant aligned = 1 n ( z z+1 )+C= 1 n ( x^n x^n+1 )+C