Mathematics

Evaluate: $$\displaystyle \int \dfrac x{1-x^2} dx$$


SOLUTION
$$I=\displaystyle \int \dfrac{x}{1-x^2}dx$$

$$t=1-x^2\implies dt=-2x dx$$

$$=\displaystyle \int -\dfrac 12\dfrac 1t dt$$

$$=-\dfrac 12\log t$$

$$=-\dfrac 12\log (1-x^2)+c$$
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Subjective Medium Published on 17th 09, 2020
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