Integration Question, w/ Trig substitution.
My question is, can I use trig sub. with a cubed root? I.e $$\sqrt[3]{x^2+1} $$

Question

Integration Question, w/ Trig substitution. 
My question is, can I use trig sub. with a cubed root? I.e $$\sqrt[3]{x^2+1}    $$

anonymous · Answer

I've got all the work done. I guess I'm just verifying that it is indeed alright. For instance in this case to use $$x=\tan \theta$$

anonymous · Answer

$cos^2\theta + sin^2\theta = 1$, divide by $cos^2\theta$
$1 + tan^2\theta = sec^2\theta$, now if u call:
$x = tan\theta$, we get:
$\sqrt[3]{sec^2\theta}$

anonymous · Answer

and $dx = sec^2\theta d\theta$

anonymous · Answer

is this answer your question?

anonymous · Answer

I guess my question was a "non-question" now that I read it again. Trig sub is just ideal for situations such as square roots because you can easily get squared values through trig identities. Sadly I made a mistake in my work where, out of habit of using the square root for trig sub, I took the root of squared tan(theta) which is incorrect considering it's a cubed root function. Thanks for making me see it. Cheers

anonymous · Answer

Np ;)