NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

The value of ∫ x d x ( x + 3 ) x + 1 is (where, c is the constant of integration)

Options

A2 x + 1 + 3 t a n - 1 x + 1 + c
B2 x + 1 + 3 2 t a n - 1 x + 1 2 + c
C2 x + 1 - 3 2 t a n - 1 x + 1 2 + c
D2 x + 1 - 3 t a n - 1 x + 1 + c

Correct answer

C. 2 x + 1 - 3 2 t a n - 1 x + 1 2 + c

Step-by-step solution

Substitute x + 1 = t , we get, 2 ∫ t 2 - 1 t 2 + 2     d t = 2 t - 6 ∫ 1 t 2 + 2   d t = 2 t - 3 2 t a n - 1 t 2 + c = 2 x + 1 - 3 2 t a n - 1 x + 1 2 + c

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