Integrate the function: 2 x 1+x^ 2 - Vidyadip

Question

Integrate the function: $\frac{2 x}{1+x^{2}}$

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Answer

Let 1 + x² = 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 + x²| + C
= log (1 + x²) + C

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