We have, I=∫2x(1+x^2) dx Let t=1+x^2 dt=2x dx Therefore, I=∫dtt I=ln t+C On putting the value of t , we get I=ln (1+x^2)+C Hence, ...

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Parametric Differentiation

∫2x1+x2 dx

Question

$\int \frac{2 x}{(1 + x^{2})} d x$

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Solution

We have,
$I = \int \frac{2 x}{(1 + x^{2})} d x$

Let
$t = 1 + x^{2}$
$d t = 2 x d x$

Therefore,
$I = \int \frac{d t}{t}$

$I = ln t + C$

On putting the value of $t$ , we get
$I = ln (1 + x^{2}) + C$

Hence, this is the answer.

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