Question

integral (e^2x -2)/(e^2x +3)
please help

Answer 1

Might be able to use integration by parts, but it easier to see if you just multiply it out and then integrate

Answer 2

\[\int\frac{e^{2x}-2}{e^{2x}+3}dx\]Let \(u = e^{2x}+3\) => \(e^{2x} = u-3\)
\[du = 2e^{2x}dx\]\[dx = \frac{du}{2e^{2x}} = \frac{du}{2(u-3)}\]
Then, the integral becomes,
\[\int\frac{(u-3)-2}{u}(\frac{du}{2(u-3)})\]\[=\frac{1}{2}\int \frac{u-5}{u(u-3)}du\]
Can you proceed from here?

Answer 3

please proceed

Answer 4

ok ok ok never mind i got it