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

Question

experimentx · Answer

separate and integrate ...

experimentx · Answer

http://www.wolframalpha.com/input/?i=integrate+%288e%5E%284y%29%2B%282y%2B3%29%29dy Click show steps to view more

sburchette · Answer

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 $$2e^{4y}+y^2+3y+C$$