Question

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?

Answer 1

anyone?

Answer 2

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.

Answer 3

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

Answer 4

Read here: http://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx
or here: http://www.intmath.com/methods-integration/8-integration-trigonometric-substitution.php

Answer 5

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

Answer 6

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?

Answer 7

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

Answer 8

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