Mathematics Homework Help with integration?

Posted on 2014-12-15 07:17:00 in Math by BELLY

When I tried to do this integration:
integrate (F / (M-At)) dt
I tried it in two ways, both involving u substitution:

Q 1.) Let's say that u = M-At
t = (M-u)/A
dt = -1/A du
Therefore:
integrate (F / (M-At)) dt = integrate (-F / uA) du = (-F/A) x ln (M-At) + C

Q 2.) Let's say that u = F / (M-At)
t = (M/A) - (F/uA)
dt = F / ((u^2)A) du
Therefore:
integrate (F / (M-At)) dt = integrate (F / uA) dt = (F/A) x ln (F / (M-At)) + C

(note: x^n means "x to the power of n")

These two answers are very different, yet involves the same technique. What is the correct answer and why?

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