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#