Given, ∫1 x^21+x^2dx =1 x^2+(1+x^2)1+x^2 1 Therefore, =∫ (21+x^2 1 #160; )dx =∫21+x^2dx ∫ 1dx =2arctan(x) x+C Hence, this is the answe ...

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Eccentric Angle : Ellipse

∫ 1- x 2 1+ x...

Question

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

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Solution

Given,
$\int \frac{1 - x^{2}}{1 + x^{2}} d x$

$= \frac{1 - x^{2} + (1 + x^{2})}{1 + x^{2}} - 1$

Therefore,
$= \int (\frac{2}{1 + x^{2}} - 1) d x$
$= \int \frac{2}{1 + x^{2}} d x - \int 1 d x$
$= 2 arctan (x) - x + C$

Hence, this is the answer.

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