Mathematics
OpenStudy (anonymous):

Intergral of 1/((x)sqrt(x^2+1)), I know i should do u-sub, my question is after i do that do i need to multiply outside the integral by 1/2 like normal or 2/1 since the x is in the denominator?

OpenStudy (anonymous):

anyone?

OpenStudy (anonymous):

You should use trigonometric substitution here. Put $$x=\tan\theta \implies dx=\sec^2\theta d\theta$$. The integral becomes then $$\int \frac{\sec^2\theta d\theta}{\tan\theta\sqrt{tan^2\theta+1}}=\int \frac{\sec\theta d\theta}{\tan\theta}=\int\csc\theta d\theta=-\log(\cot\theta+\csc\theta)$$. Now, just plug x back.

OpenStudy (anonymous):

You could use substitution $$u=x^2+1$$ if you had $$x$$ in the numerator.

OpenStudy (anonymous):
OpenStudy (anonymous):

There's another substitution you can try, $$u=\sqrt{x^2+1}$$.

OpenStudy (anonymous):

annawar I did the u sub, Do i just bring out a 1/2 in front in of integral or do i put a 2/1 since the x is in the denominator?

OpenStudy (anonymous):

What substitution did you exactly use? I mean u equal what?

OpenStudy (anonymous):

nvm i see what i did wrong, your trig sub is perfect idk why i didnt see that! ty