If the antiderivative of $\frac{1}{\sqrt{x+x^{3 / 2}}}$ is $A \sqrt{1+\sqrt{x}}+C$ then $A$ is equal to

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

If the antiderivative of

\frac{1}{\sqrt{x+x^{3 / 2}}}

A \sqrt{1+\sqrt{x}}+C

then

A

is equal to

View answer and explanation

Correct option: D

Option D (4) is correct. By substituting \

x^{1/2} = t

, the integral simplifies, leading to the antiderivative \

4 \sqrt{1+\sqrt{x}} + C

, thus A = 4.

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