∫2x1 + x^2 dx Let 1 + x^2 = t ⇒ 2x dx = dt Now the integral become ∫dtt = #160; logt + C Substituting the value of t in abo ...

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Special Integrals - 1

Evalute ∫2x...

Question

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

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Solution

$\int \frac{2 x}{1 + x^{2}} d x$
Let $1 + x^{2} = t$
$\Rightarrow 2 x d x = d t$
Now the integral become-
$\int \frac{d t}{t}$
$= log t + C$
Substituting the value of $t$ in above equation, we get
$= log (1 + x^{2}) + C$

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