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Question Number 41851 by de best last updated on 13/Aug/18

Commented by math khazana by abdo last updated on 14/Aug/18

$$changementy=atan\left(t\right)give$$$$\int \frac{dy}{a^2+y^2}=\frac{1}{a^2}\int \frac{a(1+{tan}^{2}t)dt}{1+{tan}^{2}t}(a\ne 0)$$$$=\frac{1}{a}t+c=\frac{1}{a}arctan\left(\frac{y}{a}\right)+c$$$$ifa=0weget?\int \frac{dy}{y^2}=-\frac{1}{y}+c.$$

Commented by de best last updated on 14/Aug/18

$$thankssir.reallyappreciate$$

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