{x²{{x^6+a^6}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.4
Integrate the functions in Exercises 86 to 108.

Question : 93 of 271

Marks: +1, -0

\frac{x^2}{\sqrt{x^6+a^6}}

Solution:

Let

I=\int \frac{x^2}{\sqrt{x^6+a^6}}\,dx

=\int \frac{x^2}{\sqrt{(x^3)^2+(a^3)^2}}\,dx

Put

x^3 = t \Rightarrow 3x^2\,dx = dt

\therefore I = \frac{1}{3} \int \frac{dt}{\sqrt{t^2+(a^3)^2}}

= \frac{1}{3} \log \left| t + \sqrt{t^2+a^6} \right| + C

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

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