3x²/x^6+1 - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 86 of 271

Marks: +1, -0

\frac{3x^2}{x^6+1}

Solution:

Let

I = \frac{3x^2}{x^6+1} dx

Put

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

\therefore I = \int \frac{dt}{t^2+1} = \tan^{-1} t + C

= \tan^{-1}(x^3) + C.

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