3x/1+2x^4 - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 90 of 271

Marks: +1, -0

\frac{3x}{1+2x^4}

Solution:

Let

I=\int\frac{3x}{1+2x^4}dx

Put

x^2 = t

\Rightarrow 2x dx = dt

\Rightarrow xdx = \frac{dt}{2}

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

= \frac{3}{4}\int\frac{dt}{\frac{1}{2}+t^2}

= \frac{3}{4}\int\frac{dt}{\left(\frac{1}{\sqrt{2}}\right)^2+t^2}

= \frac{3}{4} \cdot \frac{1}{\frac{1}{\sqrt{2}}} \tan^{-1}\left(\frac{t}{\frac{1}{\sqrt{2}}}\right)+C

= \frac{3}{2\sqrt{2}} \tan^{-1}(\sqrt{2}t)+C

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