(split the numerator)
(The give-away is the higher power top than bottom - or does it have to be trig?)
The problem is the integral of (x^3)/(((x^2)+16)^.5) dx x=4tan(theta)
I've worked it down to 4^2 times the integral of (tan^3(theta))/(sec(theta)) dtheta, but don't know what to do with it. Any help is appreciated.
Tom, I appreciate your pointing out of that tool for checking answers, but the way in which it gets answers is nothing like how I'm being taught and doesn't appear to be something I can replicate. tanujkush, sorry for wasting your time. I realized I had put x^2 + 16 and meant to put ((x^2)+16)^.5 on bottom. It has been fixed now.
Should also work with trig, but since you're putting another function inside x you need to multiply what you had by the derivative of the inner function, according to the chain rule, which I like to depict so...
Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).
So, the problem so far...
The chain rule also the key to the new integrand ...
Don't integrate - balloontegrate!
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