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**dokrbb** So, I have got another problem and can't figure out where is my mistake,

I have the following integral $\displaystyle \int_{2}^{5} t^{4}ln(2t)dt$, I considered $\displaystyle u = ln(2t) => u' = \frac{1}{2t}; v' = t^{4} => v = \frac{t^{5}}{5}$

and proceeded as follows: $\displaystyle \left( \frac{t^{5}}{5}ln(2t) \right) - \int\frac{1}{2t}\frac{t^{5}}{5}dt = $ here, I considered that I can do some simplifications and

obtained that $\displaystyle \left( \frac{t^{5}}{5}ln(2t) \right) - \int\frac{1}{10} t^{4}dt = \left( \frac{t^{5}}{5}ln(2t) \right) - \frac{t^{5}}{50} = $,

but by evaluating it further and doing all the math I don't get the correct answer,

I saw that and thought that I can't do the simplifications since they are still $\displaystyle u' $ and $\displaystyle v$,

so, I considered them separately, even though it seems wrong for me $\displaystyle \left( \frac{t^{5}}{5}ln(2t) \right) - \frac{t^{6} ln|2t|}{30}$ , but this also, as I expected, wrong,

please, can someone show me the mistake(s)?