x/9-4x² - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.2
Integrate the functions in Exercises 23 to 59.

Question : 37 of 271

Marks: +1, -0

\frac{x}{9-4x^2}

Solution:

Let

I = \int \frac{x}{9-4x^2} dx

Put

9 - 4x^{2} = t

\Rightarrow -8x dx = dt

\therefore I = -\frac{1}{8} \int \frac{dt}{t} = -\frac{1}{8} \log|t| + C

= \frac{1}{8} \log \frac{1}{|t|} + C

= \frac{1}{8} \log \frac{1}{|9-4x^{2}|} + C

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