# Calculus - Partial Fractions

What is the integral of

7e^(7t)

Divided By

e^14t+13e^7t+36

Using partial fractions

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1. 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

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2. Thank you so much.

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3. I've reached the last step of

(7/5) ln((x+4)/(x+9)

But how do I substitute the variable 't' back in?

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4. t = Log(x)/7 ---->

x = exp(7 t)

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