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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals2 Marks
Question
Integrate the function: $\frac{2 x}{1+x^{2}}$
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Answer

Let $1 + x^2 = t$
$\Rightarrow$ 2x dx = dt
Now, $\int \frac{2 x}{1+x^{2}} d x=\int \frac{1}{t} d t$
$= \log |t| + C$
$= \log |1 + x^2| + C$
$= \log (1 + x^2) + C$

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