Here's the problem: indefinite integral of (-3x^2)/sqrt((t^3)-16)
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Here's the problem: indefinite integral of (-3x^2)/sqrt((t^3)-16)
Are we integrating with respect to x or t? I suspect you mean for the two variables to be the same, and if so, let u be the value under the radical, and you will find you can easily get du as part of the integral.
Yes, I meant them to be the same, oops!
I got the answer to be sqrt((t^3)+16)/2 + C, but I don't think that's correct...
If you are unsure of your result, use differentiation to check your result:
We can see it is close (essentially the wrong constant factor of the radical), but not quite right. I would let:
and so we have:
Now, checking by differentiation, we find:
The derivative of the anti-derivative is the original integrand, so our result is correct.