I understand the basics of anti-derivatives, and have been given the following questions:
1: $ \int [t^3 - 5e^t - 4\cos(t)] dt $
My answer:
$ \frac{t^4}{4} - e^{5t} + \sin(4t) + c $
2: $ \int [\frac{8}{x} + 5\sec(x)\tan(x)] dx$
My answer:
$8\ln(x) + \sec^2(5x) + c$
3: $ \int \frac{4x}{(x^2 +5)^3} dx $
My answer:
None yet, slightly confused since it's a quotient.
4: $ \int [x^2 \sqrt{2x^2 + 5}] dx $
My answer:
None yet, confused as well.
So I'm wondering if someone can check number 1 & 2, and then explain/show 3 & 4?
EDIT
These are what I get when I redo them (I've done my best to just look at suggestions rather than answers):
1: $ \frac{t^4}{4} - 5e^t - 4sin(t) + c $
2: $ 8ln(x) + 5sec(x) + c $
3: $ 2 \frac{(x^2 + 5)^{-2}}{-2}$
4: $ \frac{1}{6} \frac{(2x^3 + 5)^{3/2}}{3/2}$