Question

Help please!

solve the definite integral

integral of e^(2x)/(1+e^(2x)) dx from 2 to 4

Answer 1

Do a u-sub.

Answer 2

so the u value would be 1+e^(2x)?

Answer 3

Yes, now find what du would be.

Answer 4

so du=2(e^(2x)) dx

Answer 5

which then becomes 1/2du=e^(2x)dx

Answer 6

Right! So now all you have to integrate is
\[\LARGE \frac{1}{2} \int \frac{1}{u}~du\]

Answer 7

Forgot the limits
\[\LARGE \frac{1}{2} \int_{2}^{4} \frac{1}{u}~du\]

Answer 8

so that would be...

\[1/2 \int\limits_{2}^{4}\ln u\]

Answer 9

oops sorry i mean \[(1/2)\ln(u)\]

Answer 10

Yup, now plug in what u is and evaluate it..
\[\LARGE \frac{ln|1+e^{2x}|}{2}|_{2}^{4}\]

Answer 11

so the answer would be...about 2

Answer 12

1.9910927 to be exact, but approx 2 yes :)

Answer 13

awesome :D would leaving it just at 2 be ok?

Answer 14

Depends on what your instructions or instructor wants.. USUALLY they like rounded decimal answers. But just 2 should be fine.

Answer 15

ok awesome :) thank you so much!

Answer 16

You're welcome, and good luck! :P