Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202021 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual

( (x+1)^2 x (x^2+1 ) d x= )

Options

  1. A( [x (x^2+1 ) ]+c )
  2. B( |x|+c )
  3. C( |x|+2 ⁻¹(x)+c )
  4. D(2 |x|+ ⁻¹(x)+c )

Correct answer

C. ( |x|+2 ⁻¹(x)+c )

Step-by-step solution

( aligned I & = (x+1)^2 x (x^2+1 ) d x= (x^2+1 )+2 x x (x^2+1 ) d x & = 1 x d x+2 d x x^2+1 = _e|x|+2 ⁻¹ x+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