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

Prove [tex]\int_0^{1} \frac{1}{\sqrt{x^2+6x+25}} = ln(\frac{1+\sqrt{2}}{2})[/tex]

2. Relevant equations

3. The attempt at a solution

[tex]\int_0^{1} \frac{1}{\sqrt{x^2+6x+25}}

= \int_0^{1} \frac{1}{\sqrt{(x+3)^2+16}}[/tex]

Let [tex]x+3=4tan\theta[/tex] so that [tex]dx=4sec^2\theta d\theta[/tex]

and so the problem becomes

[tex]\int \frac{4sec^2\theta}{\sqrt{16tan^2\theta+16}} d\theta[/tex]

giving [tex]\int sec\theta d\theta = ln|sec\theta + tan\theta|+ K[/tex]

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# Homework Help: Is this a good substitution that will work

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