∫〖(5x^4 ln⁡〖x^5)dx〗〗 evaluate in parts

Question

∫〖(5x^4  ln⁡〖x^5)dx〗 〗 evaluate in parts

anonymous · Answer

$$	∫〖(5x^4  \ln⁡〖x^5)dx〗 〗$$

anonymous · Answer

$$	∫▒〖(5x^4  \ln⁡x^5)dx〗 〗$$

anonymous · Answer

evaluation in parts is key here is an example

anonymous · Answer

attachment

anonymous · Answer

$$
\begin{eqnarray*}
\int 5x^4 \ln(x^5)\ dx  &=&
5\int x^4 \ln(x^5)\ dx \&=&
\ln(x^5)x^5 - 5\int x^4\ dx \ &=&
\ln(x^5)x^5 - x^5
\end{eqnarray*}
$$

anonymous · Answer

x/4 + 1/12x^3

anonymous · Answer

Wolfram agrees with me: http://www.wolframalpha.com/input/?i=integral+of+5x^4*ln%28x^5%29

anonymous · Answer

one sec i will post a very close example and you guys see if you can write it out in that format

anonymous · Answer

attachment

anonymous · Answer

From Mathematica 8 Home Edition:$$\int\limits 5x^4\text{Log}\left[x^5\right]dx=5 \left(-\frac{x^5}{5}+\frac{1}{5} x^5 \text{Log}\left[x^5\right]\right)  $$$$\text{Simplify}\left[5 \left(-\frac{x^5}{5}+\frac{1}{5} x^5 \text{Log}\left[x^5\right]\right)\right]=x^5 \left(-1+\text{Log}\left[x^5\right]\right)=x^5 \log \left(x^5\right)-x^5  $$