an integral question?

Question

how do u integrate this??

∫5e^4x/(x+2) dx??

Answer 1

ok, i will assume it is 5xe^(4)/(x+2)


since 5 and e^4 are constants, you can factor them out for now, so the integral is x/(x+2)

now here is the tricky part
literally add 2 and subtract 2 in the numerator, so
(x+2-2)/(x+2) then separate them so
(x+2)/(x+2)-2/(x+2)
now take the integrals like this
integral(1) - integral(2/x+2)
x-2*ln(absolute value(x+2))
so now you have
5e^(x)*[x-2*ln(abs(x+2))] +C

If you meant the integral as 5e^(4x)/(x+2), then the most you can do is factor out the 5, otherwise, it is not possible to take the integral

Answer 2

This is ambiguous. You didn't use enough parentheses. I assume you mean

∫5(e^4)x/(x + 2) dx

Now pull the constants out of the integral and we have

5(e^4)∫{x/(x + 2)}dx = 5e^4∫{1 - 2/(x + 2)}dx
= 5e^4{x - 2ln|x + 2|} + C

Answer 3

uuuuuuuuuuhhhhhhhhhh..........

me no know