How do I evaluate $int5y ln (9y) dy$ ?

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Answer 1 · 2015-01-30T17:18:56

I would use integration by parts where you have:

$intf(y)*g(y)dy=F(y)*g(y)-intF(y)*g'(y)dy$

Where:

$F(y)=intf(y)dy$
$g'(y)$ is the derivative of $g(y)$

In your case you can choose:

$f(y)=5y$
$g(y)=ln(9y)$

And so:

$int5y*ln(9y)dy=5y^2/2*ln(9y)-int5y^2/2*1/(9y)*9dy=$
$=5y^2/2*ln(9y)-int5y/2dy=$
$=5y^2/2*ln(9y)-5/4*y^2+c$

How do I evaluate int5y ln (9y) dyint5y ln (9y) dy?