Integration by part and definate integrate

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. :D

Re: integration by part and definate integrate

integral - Wolfram|Alpha

use this to check results

Greetings

Re: Integration by part and definate integrate