Integral involving trigonometric transformation

[fervent egret]

So idk what to do next at this point. Can u guys help me? thanks

[brisk cape]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[sharp nymph]

Uuuuh you can't manipulate the square-root like that.
$\sqrt{x^3+x} \neq \sqrt{x^3}+\sqrt{x}$

[tough sandal]

Lumberdude #LeaveWolfAsHeIs

[sharp nymph]

Have you tried rewriting it in another way. Like rewriting it in terms of sines and cosines?

[fervent egret]

Ohh good idea thanks ima do that

[gritty siren]

@fervent egret has given 1 rep to @sharp nymph

[fervent egret]

@sharp nymph sry 1 last question regarding with this

[sharp nymph]

Don't say sorry, go ahead

[fervent egret]

Do you think it's possible to solve this by using either the:
cot x = (csc^2(x) - 1)^1/2
Or
csc x = (1 + cot^2(x) ) ^1/2
?

[sharp nymph]

Honestly, the first thing I'd try is just writing it out in terms of sines and cosines

[sharp nymph]

I don't know those suggestions you gave would work because the sqrt in the problem makes it extra hard if you introduce another one inside

[fervent egret]

I don't think there's other way too bcs I've already tried both but like they're leaving me dead end ithink

[sharp nymph]

That would make substitution hard

[fervent egret]

Yeah I dont think so as well bcs my professor just introduced us new topic which is transformation of trigs

[sharp nymph]

Looks good!

[fervent egret]

Basically the usage of sin 2 x + cos 2 x = 1

And the csc sec cot andtan

[sharp nymph]

Those can be quite helpful!

[fervent egret]

To make the integrands integrable

Yeah

But I Dont think that one's so lol

[sharp nymph]

Even for integrals that don't have any trig functions inside of them

You can sub in a trig function and then solve that way sometimes

[fervent egret]

Yeah to be able to take away the trig function that is beside it too

[sharp nymph]

No, to introduce trig functions even

[fervent egret]

Wdym?

[sharp nymph]

Like integrals of the form

$\int \frac{dx}{\sqrt{x^2-1}}$

[fervent egret]

Ohh yeah right

Ur gonna use an inverse trig formula there

Alright man gtg

[sharp nymph]

Yo ttyl man

Have a nice evening

[fervent egret]

Nice chatting with u gotta sleep lol