Integration help?

[klooless]

I don't understand how to go about integrating this:

?x (?(4+x^2)) dx

any guidance would be great!

cheers.

 

[pka]

Is the problem \(\displaystyle \int {x\sqrt {4 + x^2 } dx}~?\)

 

[galactus]

If that is it, try letting \(\displaystyle x=2tan{\theta}, \;\ dx=2sec^{2}{\theta}d{\theta}\)

 

[klooless]

Thank you galactus, that is it. But I don't see how tan x or sec^2 x can be used since there is a 4 in the denominator and it's (+) x^2, not (-) x^2...

I appreciate the help so far!

 

[pka]

That is it.

Let \(\displaystyle u=4+x^2~\&~du=2xdx\)
Then you have \(\displaystyle \int {\frac{{\sqrt u }}{2}du}\).

 

[galactus]

Because \(\displaystyle tan^{2}(x)+1=sec^{2}(x)\)

\(\displaystyle \sqrt{4+(2tan(t))^{2}}=\sqrt{4+4tan^{2}(t)}=\sqrt{4(1+tan^{2}(t))}=2\sqrt{sec^{2}(t)}=2sec(t)\)

 

[Deleted member 4993]

There are many ways to skin the same cat - pka and galactus had shown you two different ways to get the same answer.