Question

x^​2/​(x^​2+​4)^​2 integrate

Answer 1

Any ideas of how to begin?

Answer 2

is the ^2 for the whole thing?

Answer 3

\[\Large \sin^2 \theta + \cos^2 \theta = 1\] Let's divide both sides of the equality by cos^2 theta.\[\Large \frac{\sin^2 \theta}{\cos^2\theta} +\frac{ \cos^2 \theta}{\cos^2\theta} = \frac{1}{\cos^2\theta}\] Well that's just some other trig functions:\[\Large \tan^2 \theta + 1 = \sec^2 \theta\]

Now let's manipulate the first one and this one around into three different forms:

\[\Large \sec \theta = \sqrt {\tan^2 \theta + 1}\]\[\Large \tan \theta = \sqrt{\sec^2 \theta -1}\]\[\Large \cos \theta = \sqrt{1-\sin^2 \theta}\]

Notice we have a square root with three possible ways to have something next to it. Look at how the negative signs match this pattern: \[\Large \sqrt{x^2+1}\]\[\Large \sqrt{x^2-1}\]\[\Large \sqrt{1-x^2}\]

Answer 4

Your move. I'll be back in about 15 to 30 minutes to see what you've figured out.