What is $int e^5x/5$ ?

Question

$int e^5x/5$

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Answer 1 · 2018-05-04T09:14:55

Your question is :

$I=inte^5x/5$

$(i)$ If it is: $I=inte^5x/5dx$ ,then

$I=e^5/5intxdx=e^5/5(x^2/2)+c=e^5/10x^2+c$

$(ii)$ If it is : $I=inte^(5x)/5dx,then,$

$I=1/5inte^(5x) dx=1/5(e^(5x)/5)+c=1/25e^(5x)+c$

Note;

For $inte^(5x)dx$ , take, $5x=u=>x=1/5u=>dx=1/5du$

So, $inte^(5x)dx=inte^uxx1/5du=1/5e^u+c=1/5e^(5x)+c$

$=>I=1/5(1/5e^(5x))+c=1/25e^(5x)+c$