Question

find the integral (8e^(4y)+(2y+3))dy

Answer 1

separate and integrate ...

Answer 2

http://www.wolframalpha.com/input/?i=integrate+%288e%5E%284y%29%2B%282y%2B3%29%29dy
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Answer 3

Assuming I read the equation correctly, I see\[\int\limits(8e^{4y}+2y+3)dy\]
You can integrate this term by term. The last two aren't much trouble, but you'll have to use u substitution to integrate the first term. You can let 4y=u which implies tht 4dy=du. You can set up the first term as (pulling out the 8 to the front)\[2\int\limits\limits e^udu\]This gives us \[2e^u\] Substituting 4y back in for u you get \[2e^{4y}\] Now you can add that to the integral of the remaining terms to obtain \[2e^{4y}+y^2+3y+C\]