Question

integration of exponential functions

Answer 1

Since it's in respect to z, use a sub: \(u=1+e^z\)

Answer 2

Thank you =)

Answer 3

@Luigi0210 is it okay if i let u as my 3x? or is it 10 ^3x?

Answer 4

3x is the exponent right?

Answer 5

yes

Answer 6

wait is z in complex plane ?

Answer 7

i got dx= 1/3 du if i let u as 3x

Answer 8

You might need to make two subs~
\[\Large \int \sqrt{10^{3x}}~dx\]
\(u=3x\) so \(du=3dx\)
\[\Large \int \sqrt{10^u}~du\]
From here you could integrate or use another sub of \(\Large a=\frac{u}{2}\)

Answer 9

Sorry, \(\Large \frac{1}{3} \int \sqrt{10^u}~du\) not \(\Large \int \sqrt{10^u}~du\)

Answer 10

yes thats where im stuck.

Answer 11

dealing with sq roots. can you help me?

Answer 12

He is helping you.

Answer 13

Change it to \[\Large \int 10^{u/2}~du\]

Use \(a=\frac{u}{2}\) so \(da=\frac{1}{2}du\)

So now you just deal with
\[\Large \int 10^a~da\]

Answer 14

Dang it, sorry, I keep forgetting the constant, it's \(\Large \frac{2}{3}\)

Answer 15

Think you can integrate \(\Large \frac{2}{3} \int 10^a~da\)?

Answer 16

how come its 2/3?

Answer 17

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The 3 from the u sub \(==>\frac{1}{3}\)

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The \(\frac{1}{2}\) from the a sub \(==> 2\)

So \(\Large \frac{1}{3}*2\)

Answer 18

ah yes yes. wait' ill solve this first. =)

Answer 19

i got 2/3 (10^a + c)