MHT CET202618 April 2026Morning ShiftMathematicsIndefinite IntegrationActual
The value of n cosec ^2 x^n - 1 x^ (1-n) ,dx is ...
Options
- A( x) + c
- B( x^n) + c
- C( x^n) + c
- D( x^n) + c
Correct answer
B. ( x^n) + c
Step-by-step solution
Let the given integral be I = n cosec ^2 x^n - 1 x^ (1-n) ,dx Using the trigonometric identity cosec ^2 - 1 = ^2 , the integral simplifies to: I = n x^n x^ 1-n ,dx I = n x^ n-1 x^n ,dx Let x^n = t , which gives n x^ n-1 ,dx = dt . Substituting these into the integral, we get: I = t ,dt I = ( t) + c Substituting t = x^n back into the expression: I = ( x^n) + c Answer: ( x^n) + c