integrate (1/(sqrt(x^2+10))dx

Question

ganeshie8 · Answer

trig substitution

ganeshie8 · Answer

maybe, sub $x = \sqrt{10} \tan \theta$

anonymous · Answer

for substitution, what is your u?

anonymous · Answer

@ganeshie8 ^^^^

hartnn · Answer

so, you're comfortable with 'u'

from ganeshie's sub.,
x = sqrt 10 tan u 
gives
$ u =  \tan^{-1}(x/\sqrt {10}) $

ganeshie8 · Answer

$\large \mathbb{ \int \frac{1}{\sqrt{x^2+10}}}dx$

sub $x = \sqrt{10} \tan \theta$
$dx = \sqrt{10} \sec^2 \theta d\theta$

$\large \mathbb{ \int \frac{\sqrt{10}\sec^2\theta d\theta}{\sqrt{10 \tan^2\theta +10}}}$

$\large \mathbb{ \int \frac{\sec^2\theta d\theta}{\sqrt{ \tan^2\theta +1}}}$


$\large \mathbb{ \int \frac{\sec^2\theta d\theta}{\sqrt{ \sec^2\theta}}}$

$\large \mathbb{ \int \sec \theta d\theta}$

ganeshie8 · Answer

simplifies to that,
after that u may pull the integral of sec as formula :

$\large \int \sec x    =    \ln|\sec x + \tan x| + C $

ganeshie8 · Answer

and dont forget to convert the theta's in final answer...