Can someone help me with this?

Integrate e^x/(e^x+4)

Question

Can someone help me with this?

Integrate e^x/(e^x+4)

lgbasallote · Answer

hint!!

let u = e^x

do a u substitution ;)

anonymous · Answer

u = e^x + 4
du = e^x dx

integrate 1/u du ... i think

lgbasallote · Answer

yup that's right @dedee :)

lgbasallote · Answer

do you know how to proceed now @Saltin8R ?

anonymous · Answer

not sure how this works do i answer or just help?

anonymous · Answer

Not exactly. Is there a certain rule for integrating 1/u? Coz that's just the same as u^-1, which would integrate to 1.

lgbasallote · Answer

you just help :) @dedee as much as possible ^_^

anonymous · Answer

yeah it should be listed in the back of your book or on a reference page

lgbasallote · Answer

yes there is a rule to 1/u

it is the exception to the power rule

$$\int \frac{1}{f(x)} = \ln |f(x)| + c$$

got that @Saltin8R ?

anonymous · Answer

d/dx ln(x) = 1/x   =)

lgbasallote · Answer

the power rule is $$\int f(x)^n = \frac{f(x)^{n+1}}{n+1}$$ however..if n would be -1 then the denominator would be 0 garnering undefined..thus u^-1 is the exception

anonymous · Answer

yes, thanks guys :) I've got the correct answer :)

lgbasallote · Answer

congradumations ^_^