JEE Main2016MathematicsIndefinite IntegrationActual
The integral ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x , is equal to
Options
- Ax 5 2 x 5 + x 3 + 1 2 + c
- B- x 10 2 x 5 + x 3 + 1 2 + c
- C- x 5 x 5 + x 3 + 1 2 + c
- Dx 10 2 x 5 + x 3 + 1 2 + c
Correct answer
D. x 10 2 x 5 + x 3 + 1 2 + c
Step-by-step solution
Given, I = ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x = ∫ 2 x 12 + 5 x 9 d x x 15 1 + 1 x 2 + 1 x 5 3 = ∫ 2 x 3 + 5 x 6 d x 1 + 1 x 2 + 1 x 5 3 Let, 1 + 1 x 2 + 1 x 5 = t ⇒ - 2 x 3 - 5 x 6 d x = d t ⇒ 2 x 3 + 5 x 6 d x = - d t I = - ∫ d t t 3 = 1 2   .   t 2 I = 1 2 1 1 + 1 x 2 + 1 x 5 2 + c = 1 2 x 10 x 5 + x 3 + 1 2 + c Where c is the constant of integration. = x 10 2 x 5 + x 3 + 1 2 + c