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Question Number 105743 by Skabetix last updated on 31/Jul/20

Commented by Skabetix last updated on 31/Jul/20

$$thankyouinadvance$$

Answered by john santu last updated on 31/Jul/20

$$\underset{a}{\stackrel{b}{\int }}\frac{\frac{df\left(x\right)}{dx}}{\sqrt{1+f^2\left(x\right)}}dx+f^3\left(b\right)-f^3\left(a\right)$$$$\underset{a}{\stackrel{b}{\int }}\frac{df\left(x\right)}{\sqrt{1+f{}^2\left(x\right)}}+f{}^3\left(b\right)-f{}^3\left(a\right)$$$${[\ln \mid f\left(x\right)+\sqrt{1+f{}^2\left(x\right)}\mid ]}_a^b+f{}^3\left(b\right)-f{}^3\left(a\right)$$$$\ln \mid \frac{f\left(b\right)+\sqrt{1+f{}^2\left(b\right)}}{f\left(a\right)+\sqrt{1+f^2\left(a\right)}}\mid +f{}^3\left(b\right)-f^3\left(a\right)$$

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