Indefinite integral substitution

[sapiental]

evaluate the indefinite integral ((e^x)/((e^x)+1))dx

I let u = ((e^x)+1)

then

du = (e^x)dx

which occurs in the original equation so..

indefinite ingegral ((u^-1)du)

taking the antiderivative I get 1 + C

is this right? thanks!

 

[courtrigrad]

$$\int \frac{e^{x}}{e^{x}+1} dx$$

it should be $$\ln|e^{x}+1| + C$$ because it is of the form $$\int \frac{du}{u}$$