Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202421 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

e^x ( x+2 x+4 )^2 d x=

Options

  1. A- x e^x (x+4)^2 +c
  2. B- x e^x (x+4) +c
  3. Cx e^x (x+4) +c
  4. D2 x e^x (x+4) +c

Correct answer

C. x e^x (x+4) +c

Step-by-step solution

aligned & I = ( x+2 x+4 )^2 e^x d x= e^x [ x^2+4+4 x (x+4)^2 ] d x & I = e^x x (x+4) d x+ 4 e^x (x+4)^2 d x aligned Integrating by parts I =e^x ( x x+4 )- 4 e^x (x+4)^2 d x+ 4 e^x d x (x+4)^2 I = x e^x x+4 +c

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