(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]Evaluate $\displaystyle\int^{1}_{0}{\sqrt{x^2+1}}$[/tex]

2. Relevant equations

3. The attempt at a solution

[tex]By trigonometric substitution: $x = \tan{\theta} \rightarrow dx = \sec^2{\theta}\,d\theta$

\[\int^{\frac{\pi}{4}}_{0}{\sec^2{x}\sqrt{\tan^2{\theta}+1}}\,d\theta = \int^{\frac{\pi}{4}}_{0}{\sec^3{\theta}}\,d\theta\]

\[= \int^{\frac{\pi}{4}}_{0}{\sec{\theta}\tan^2{\theta}+\sec{\theta}}\,d\theta\][/tex]

This is where I get stuck

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# Integral problem

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