thank you i solved the problem

[icyhot2590]

thank you i solved the problem

 

[stapel]

"Evaluate" over what interval or at what values? ("Evaluate" requires inputs, which I'm not seeing in your post.)

When you reply, please include a clear listing of everything you have tried so far. Thank you.

Eliz.

 

[stapel]

this is what i have done

e^(1/(x+1))(u)^-2
u=1-x+1
f(u) = e^(1/(x+1)) (u) ^-2

I'm sorry, but I don't understand what you are doing. It almost looks like you are "finding the integral", rather than "evaluating" a completed integration.

Please clarify. Providing the complete instructions and a clear explanation of your steps would probably be helpful. (Please also "Reply" with your replies. Edits are usually overlooked.)

Thank you.

Eliz.

 

[soroban]

Re: evaluate the integral of e^(1/(x+1))/(x+1)^2

Hello, icyhot2590!

\(\displaystyle \L\int \frac{e^{\frac{1}{x+1}}} {(x\,+\,1)^2}\,dx\)

Let \(\displaystyle u\:=\:\frac{1}{x\,+\,1} \:=\x\,+\,1)^{-1}\;\;\Rightarrow\;\;du\:=\:-(x\,+\,1)^{-2}\,dx\;\;\Rightarrow\;\;dx\:=\:-(x\,+\,1)^2\,du\)

Substitute: \(\displaystyle \L\:\int\frac{e^u}{(x\,+\,1)^2}\,\cdot\,\)\(\displaystyle \left[-(x\,+\,1)^2\,du\right] \;=\;-\L\int\)\(\displaystyle e^u\,du \;=\;-e^u\,+\,C\)


Back-substitute: \(\displaystyle \L\:-e^{\frac{1}{x+1}} \,+\,C\)

 

[icyhot2590]

thank u for helping me