Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2024MathematicsIndefinite IntegrationActual

1+x+ x+x^2 x + 1+x d x is equal to

Options

  1. A1 2 1+x +C
  2. B2 3 (1+x)^ 3 2 +C
  3. C2(1+x)^ 3 2 +C
  4. D1+x +C

Correct answer

B. 2 3 (1+x)^ 3 2 +C

Step-by-step solution

Let I = 1+x+ x+x^2 x + 1+x dx . Observe that the numerator can be written as 1+x+ x 1+x = 1+x ( 1+x + x ) . Substituting this into the integral, we get I = 1+x ( 1+x + x ) x + 1+x dx . Canceling the common term ( x + 1+x ) , the integral simplifies to I = 1+x dx . Using the power rule for integration, (1+x)^ 1/2 dx = (1+x)^ 3/2 3/2 + C . Therefore, I = 2 3 (1+x)^ 3/2 + C . Answer: 2 3 (1+x)^ 3 2 +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 COMEDK PYQs