Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201726 Apr 2017Morning ShiftMathematicsIndefinite IntegrationActual

5 x^2+3 x^2 (x^2-2 ) d x=

Options

  1. A13 2 2 | 2 -x 2 +x |+ 3 2 x +C
  2. B13 4 2 | x+ 2 x- 2 |+ 3 2 x +C
  3. C13 4 2 | x- 2 x+ 2 |+ 3 2 x +C
  4. D5 3 2 | x+ 2 x- 2 |+ 3 5 x+C

Correct answer

C. 13 4 2 | x- 2 x+ 2 |+ 3 2 x +C

Step-by-step solution

Let, I= 5 x^2+3 x^2 (x^2-2 ) d x Put x^2=y . Then, aligned & 5 y+3=(y-2) A+y B & 5 y+3=y(A+B)-2 A aligned On comparing the coefficients, we get A+B=5 and 3=-2 AA= -3 2 and B= 13 2 Thus, 5 y+3 y(y-2) = 5 x^2+3 x^2 (x^2-2 ) =- 3 2 1 x^2 + 13 2 1 x^2-2 Now, I=- 3 2 d x x^2 + 13 2 d x x^2-2 gathered =- 3 2 (- 1 x )+ 13 2 1 2 2 | x- 2 x+ 2 |+C = 3 2 x + 13 4 2 | x- 2 x+ 2 |+C gathered

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