If $\int \sqrt{\frac{x^4}{a^6+x^6}} d x=g(x)+C$, then $g(x)=$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \sqrt{\frac{x^4}{a^6+x^6}} d x=g(x)+C

, then

g(x)=

View answer and explanation

Correct option: C

\frac{1}{3} \log \left|x^3+\sqrt{a^6+x^6}\right|

Option C,

\frac{1}{3} \log \left|x^3+\sqrt{a^6+x^6}\right|

, is the correct antiderivative obtained by substitution and using the integral formula for

\int \frac{1}{\sqrt{u^2+a^2}} du

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{C}

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