Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201923 Apr 2019Morning ShiftMathematicsIndefinite IntegrationActual

If (I_ m, n = e^ m x x^n d x ), then (I_ m, n + n m I_ m, n-1 = )

Options

  1. A(x^n e^ m x +c )
  2. B( x^n e^ m x n +c )
  3. C( x^n e^ m x m +c )
  4. D( -x^n e^ m x m +c )

Correct answer

C. ( x^n e^ m x m +c )

Step-by-step solution

( aligned & I_ m, n = e^ m x x^n d x & = 1 m x^n e^ m x - (n x^ n-1 ) ( e^ m x m ) d x & = x^n e^ m x m - n m e^ m x x^ n-1 d x= x^n e^ m x m - n m I_ m, n-1 +c & I_ m, n + n m I_ m, n-1 = x^n e^ m x m +c aligned ) Hence, option (c) is correct.

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

If 5 x x -2 dx = ax + b | x -2 x |+ c , then a + b = 2025x Cos ⁻¹ ( 1-x^2 1+x^2 ) d x(x>0)= 2025d x (1+ x ) x-x^2 = 2025If x x x+1 ~d x= f (x)+ k , then f ( 4 )= 2025If x^4+1 x^2+1 d x=A x^3+B x^2+C x+D Tan ⁻¹ x+E , then A+B+C+D= 2025If x^2-x+2 x^2+x+2 d x=x- (f(x))+ 2 7 Tan ⁻¹(g(x))+c , then f (-1)+ 7 ~g (-1)= 2025(x- 3 ) (x+ 6 ) d x= 2025If a x+3 x 5 x+2 x d x= 26 29 x- k 29 |5 x+2 x|+c , then |a+k|= 2025 Full Indefinite Integration list All AP EAMCET PYQs