If $f(x)=\sqrt{x^2-a^2}$ then $\int \frac{x^2}{f(x)} \mathrm{d} x$ is

$x f(x)+\frac{a^2}{2} \log |x+f(x)|+C$

$\frac{x^2}{2} f(x)-\frac{a^2}{2} \log |x+f(x)|+C$

$\frac{x^2}{2} f(x)+a^2 \log |x-f(x)|+C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f(x)=\sqrt{x^2-a^2}

then

\int \frac{x^2}{f(x)} \mathrm{d} x

View answer and explanation

Correct option: D

\frac{x}{2} f(x)+\frac{a^2}{2} \log |x+f(x)|+C

Option D (

\frac{x}{2} f(x)+\frac{a^2}{2} \log |x+f(x)|+C

) is correct because it is the result of integrating the given function using integration by parts and trigonometric substitution.