Thread: help for integration

the question is integrate 2/(4+x^2) and it is solved by using let x = 2 tan u my problem is how do i know that i should make x = 2tanu i know integral of tan inverse = 1/(1+x^2) im confused! can anyone help me?

Originally Posted by slash

the question is integrate 2/(4+x^2) and it is solved by using let x = 2 tan u my problem is how do i know that i should make x = 2tanu i know integral of tan inverse = 1/(1+x^2) im confused! can anyone help me?

Theoretically speaking you could come up with this on your own.

Practically speaking, you didn't, so simply remember from now on that if you have an integral of the form
$\displaystyle \int \frac{dx}{a^2 + x^2}$
you can make the substitution $\displaystyle x = a \cdot tan(\theta)$.

Sometimes in order to do an integral you have to have seen how it is done first. Some people have an easier time seeing how to do these than others. There is no method I know of telling you how to approach an integral, it's a matter of experience. There is no shame in this.

-Dan

Actually, these kind of integrals are quickly to solve.

$\displaystyle \int\frac2{4+x^2}\,dx=2\int\frac1{2^2+x^2}\,dx=2\c dot\frac12\arctan\frac x2+k=\arctan\frac x2+k$

If you follow topsquark's Hint, you'll derive the general formula for these things.