JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

The integral

\int \frac{1}{(1+\sqrt{x}) \sqrt{x-x^2}} d x

is equal to (where

C

is the constant of integration)

View answer and explanation

Correct option: B

-2 \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}

Option B is correct because after using the trigonometric substitution

x = \cos^2 \theta

, the integral simplifies and evaluates to

-2 \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C

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