Question

Differentiate \[\frac{ x^2 }{ 4 }\log_{e}x \] and hence find \[\int\limits x \log_{e}x \].

Help please. I don't know to should i do this question. Can anyone help me out.

Thanks.

Answer 1

\[\frac{ d }{ dx }\left( \frac{ x^2 }{ 4 }\log_{e}x \right)=\frac{ x^2 }{ 4 }*\frac{ 1 }{ x }+\frac{ 2x }{ 4 }\log_{e } x\]
\[=\frac{ x }{ 4 }+\frac{ 2x }{ 4 }\log_{e} x\]

Answer 2

I found how to do it. Thanks for the help.

Answer 3

the answer was \[ \frac{ x^2\log_{e}x }{ 2 } -\frac{ x^2 }{ 4 }\]

Answer 4

\[\int\limits \left( \frac{ x }{ 4 }+\frac{ 2x }{ 4 }\log_{e}x \right)dx=\frac{ x^2 }{ 4 }\log_{e} x+c\]
now you can complete it.

Answer 5

Thanks.

Answer 6

yw.