Please help me to check whether the answer is correct or not.
1. ∫1/x^2 ln x dx = -1/x ln x + 1/x^2 + c
2. ∫x sin 2x dx = -x cos 2x/2 + sin 2x/4 + c
3. ∫_3^5 5/(2x-5) dx = 5/2 ln 5
4. ∫_0^π/4 (e^-2x + 2 tan x) dx = 1/2(1-e^((-π)/2)/2)
Help me to prove these two.
1. ∫_0^π/4 tan^3 x dx = (1-ln 2/2)
2. ∫_0^π/2 4/(3+5sin x) dx = ln 3
And thanks in advance, I already work on it for few hours, thus your help will be greatly appreciated.