If $$f(x)=x2$$−$$a2$$ then ∫$$x2f(x)dx$$ is

Correct option is 4x2f(x)+a22log⁡|x+f(x)|+C

Questions

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

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xf(x)+a22log⁡|x+f(x)|+C

x22f(x)−a22log⁡|x+f(x)|+C

x22f(x)+a2log⁡|x−f(x)|+C

x2f(x)+a22log⁡|x+f(x)|+C

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detailed solution

Correct option is D

I=∫x2x2−a2dx=∫x2−a2dx+a2∫dxx2−a2=12xx2−a2−12a2log⁡x+x2−a2+a2log⁡x+x2−a2+c=12xf(x)+12a2log⁡|x+f(x)|+C

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If f(x)=x2−a2 then ∫x2f(x)dx is

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