x²/1-x^6 - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 91 of 271

Marks: +1, -0

\frac{x^2}{1-x^6}

Solution:

Let

I=\int \frac{x^2}{1-x^6}\,dx

=\frac{x^2}{1-(x^3)^2}\,dx

Put

x^3 = t

\Rightarrow 3x^2\,dx = dt

\therefore I = \frac{1}{3}\int \frac{dt}{1-t^2}

=\frac{1}{3} \cdot \frac{1}{2} \log \left| \frac{1+t}{1-t} \right| + C

=\frac{1}{6} \log \left| \frac{1+t}{1-t} \right| + C

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

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