Question

Integrate (e^x)/(3+e^x)^2 dx, plz i need help and id appreciate if u can explain step through step cuz i hav no idea what im doing >.<

Answer 1

Try using a u-substitution where u=3+e^x :)

Answer 2

you use u-substitution by letting u =3+e^x. du=e^xdx

Answer 3

so u should get -(u+3)^(-1) +c

Answer 4

these sorts of integral u can solve in ur head... even without using sub method

Answer 5

\[u = 3+e^x \longrightarrow du=e^xdx \longrightarrow dx=e^{-x}du\]
\[\int\limits \frac{e^xe^{-x}du}{u}=\int\limits \frac{du}{u^2}\]
\[= -\frac{1}{u}+c\]
\[=-\frac{1}{x+e^x}+c\]

Answer 6

this is the full step by step solution