Question

calc help integral ((7)/(e^(5t)+3))(dx) show steps please

Answer 1

Do you mean dt instead of dx?

Answer 2

yeah dt sorry

Answer 3

so far ive gotten to 7 integral (1/(e^(5t)+3)) dt. I tried doing the u substitution for the denominator but it didnt look correct.

Answer 4

it is going to be a pain
you can use \(u=5x\) as a start, but that only gets you to \(\frac{7}{5}\int\frac{du}{e^u+3}\)

Answer 5

then another sub maybe as \(z=e^u, dz=e^udu,\frac{1}{e^u}dz=du\) gives
\[\int\frac{1}{z(z+3)}\]

Answer 6

this one requires partial fractions
if you have not got there yet i am not sure of another snappier way to do it

Answer 7

is there any way you would be able to explain the partial fractions to me right now?