Question

Is a/o good with in tegration by subsitution?

Answer 1

Yeah, go for it.

Answer 2

oh i think i got it but i will share it neways

Answer 3

\[\int\limits_{?}^{?}(e ^{t})/(1+e^t)\]

Answer 4

ignore the question marks though

Answer 5

sorry I have a hard time typing out the equations

Answer 6

\[\phi=1+e^t \implies d \phi =e^t dt\]
Thus the integral becomes (by direct substitution)
\[\int\limits \frac{d \phi}{\phi}=\ln|\phi|+C=\ln|1+e^t|+C\]

Answer 7

y is it in these lines? Y is it with the absolute value thingy?

Answer 8

Because you can't put negative numbers into a logarithm. So the absolute value MUST be there to ensure you don't get an complex argument.

Answer 9

ohhhh ya right. Thanks u r awesome!!!