# Math Help - integral2

1. ## integral2

integral

du/(sqrt(1+u^2) )

any help pls

2. Originally Posted by alex83
integral
$
\int \frac{du}{\sqrt{1+u^2}}$

any help pls
You can find this in a table of integrals. It's $arcsinh(u)$. (It's the "inverse hyperbolic sine of u".)

3. Originally Posted by alex83
integral

du/(sqrt(1+u^2) )

any help pls
As you'll see this is a standard trig integral, but it's better to do it by trig substitution.

Construct a right triangle with a vertical leg of u, a horizontal leg of 1 and by Pythagoras the hypotenuse is $\sqrt{1+u^2}$. Let theta be the angle such that $\tan(\theta)=u$. You will also notice that $\cos(\theta)=\frac{1}{\sqrt{1+u^2}}$, which makes an easy substitution. Make sure to calculate $d\theta$ in terms of u, then make the full substitution, integrate, then back substitute.

4. a classic problem, we can also put $v=u+\sqrt{1+u^2}.$