Question

Evaluate the follow integral and simplify the result.
∫1/((2e^x) -3)

Answer 1

\[\int \frac{1}{2e^x-3}dx\]??

Answer 2

Yes, can you help me?

Answer 3

let \(u=e^x\) => du/dx=e^{x}

Answer 4

\[\int \frac{1}{2u-3}*e^{x}du =>\int \frac{1}{u(2u-3)}du\]

Answer 5

Wait, I thought that if du/dx=e^{x}, then dx=du/e^x.

Answer 6

\[\frac{du}{dx}=e^x\]
\[du=e^{x}dx\]
\[e^{x}dx=du\]
\[dx=\frac{du}{e^x}\]

Answer 7

yeah, i made a typo..but the last part is still right.

Answer 8

So is it \[\int\limits_{}^{}\frac{ 1 }{ 2e^x-3 } \frac{ du }{ e^x }\]

Answer 9

u=e^x

Answer 10

then proceed with partial fractions.