More integration by substitution...problem below:

Question

anonymous · Answer

$$\int\limits (x^2 +1)^3 dx$$I tried u=x^2+1...no dice.

anonymous · Answer

Is there an efficient way to go about this or do I actually have to multiply it out first?

zepdrix · Answer

No you certainly don't have to multiply it out :)
That is definitely one option though, and it wouldn't be too difficult.

Alternatively you can do a trig substitution. :D
Might actually be more work though on this particular one ^^

Depends what you wanna try c:

anonymous · Answer

Ah, thought it might be trig...just watched videos on that today...

zepdrix · Answer

For trig subs you really want to have these 2 identities in the front of your mind, so you can easily recognize them when things like this show up :D
$$\sin^2x+\cos^2x=1$$$$\tan^2x+1=\sec^2x$$

Think you can get through it ok? :D

anonymous · Answer

Ah, yes, thank you @zepdrix. I can see where some of the gaps in my self-instruction are. Looks like I'm going to need to drill trig identities.

anonymous · Answer

So it looks like I'd do this: $$u=\sec^2x$$ Well, du is going to be duh for me for the moment. :) Thanks, though. I know what I need to study now.

zepdrix · Answer

Ah :)

zepdrix · Answer

|dw:1349151684474:dw|
:O