I have 3 problems dealing with the Fundamental Theorem of Calculus that I'm working on. The first one is relatively easy, but the second two are above my head. If anyone has the time to explain them, I would be thankful.
1: $ \int_1^8 [3x^3 - \frac{5}{x} + 2 \sqrt[3]{x^2} $
My Answer:
$ \int [ \frac{3*(8)^4}{4} - 5 ln(8) + \frac{2(8)^{3/2}}{3/2}] - \int [ \frac{3(1)^4}{4} - 5 ln(1) + \frac{2(1)^{5/2}}{5/2} $
2: $ \int_0^{\pi/6} (sin(3x) - cos(3x)) $
My answer:
I don't have one yet, I'm unsure of how to get the anti-derivative of a trig function with a variable larger than x.
3: $ \int_{ln(1)}^{ln(2)} \frac{e^{2x}}{e^{2x} + 4} $
My answer:
I don't know where to begin with this one. Do I do u = $e^{2x} +4$ and du = $\frac{e^{2x}}{2}$?
EDIT
Updated answers:
1: $ \int [ \frac{3*(8)^4}{4} - 5 ln(8) + \frac{2(8)^{5/3}}{5/3}] - \int [ \frac{3(1)^4}{4} - 5 ln(1) + \frac{2(1)^{5/3}}{5/3} $
2: $ \int_0^{\pi/6} \frac{1}{3}cos(3(\frac{\pi}{6})) + \frac{1}{3}sin(3(\frac{\pi}{6})) $
3: