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Question Number 27853 by Poojadarshini94 last updated on 15/Jan/18

Commented by abdo imad last updated on 17/Jan/18

$$letputf\left(x\right)=ln(x+\sqrt{x^2+a^2)}wehave$$$$f^{\prime }\left(x\right){=}^{}\frac{1+\frac{2x}{2\sqrt{x^2+a^2}}}{x+\sqrt{x^2+a^2}}=\frac{x+\sqrt{x^2+a^2}}{\sqrt{x^2+a^2}}.\frac{1}{x+\sqrt{x^2+a^2}}$$$$=\frac{1}{\sqrt{x^2+a^2}}\Rightarrow \int \frac{dx}{\sqrt{x^2+a^2}}=ln(x+\sqrt{x^2+a^2})+k$$$$anothermethodyoucanusethech.x=asht...$$

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