Mathematics


$$\displaystyle \int_{1}^{2}\frac{\mathrm{d}\mathrm{x}}{\sqrt{1+\mathrm{x}^{2}}}=$$


ANSWER

$$\displaystyle \log_{\mathrm{e}}(\frac{2+\sqrt{5}}{\sqrt{2}+1})$$


SOLUTION

$$\int_{1}^{2}\dfrac{dx}{\sqrt{1+x^2}}=\log |x+\sqrt{x^2+a}|+c$$
$$\int_{1}^{2}\dfrac{dx}{\sqrt{1+x^2}}=\log |x+\sqrt{x^2+1}|+c$$
$$=\log |2+\sqrt{5}|-\log |1+\sqrt{2}|$$
$$=\log \left | \dfrac{2+\sqrt{5}}{1+\sqrt{2}} \right |$$
$$\int_{1}^{2}\dfrac{dx}{\sqrt{1+x^2}}=\log \left | \dfrac{2+\sqrt{5}}{1+\sqrt{2}} \right |$$

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Single Correct Medium Published on 17th 09, 2020
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