Calculus  Partial Fractions
posted by Sean on .
What is the integral of
7e^(7t)
Divided By
e^14t+13e^7t+36
Using partial fractions

Substitute t = Log(x)/7
Integral is then proportional to:
Integral of dx/[x^2 + 13 x + 36] =
Integral of dx/[(x+4)(x+9)]
1/[(x+4)(x+9)] = A/(x+4) + B/(x+9)
Multiply both sides by x+4 and take limit x to 4:
1/5 = A
Multiply both sides by x+9 and take limit x to 9:
1/5 = A
1/5 = B 
Thank you so much.

I've reached the last step of
(7/5) ln((x+4)/(x+9)
But how do I substitute the variable 't' back in? 
t = Log(x)/7 >
x = exp(7 t)