is there a formula for integrating fractions??? sorry if this is hard to understand but i need to find the INTEGRAL of x/(2+e^x).

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- May 3rd 2010, 07:53 PMhelpmeeeplease help ap calc test tomorrow
is there a formula for integrating fractions??? sorry if this is hard to understand but i need to find the INTEGRAL of x/(2+e^x).

- May 3rd 2010, 08:10 PMsurjectiveintegrating fractions
Hello,

When facing such problems you should realize that:

$\displaystyle \int \frac{x}{2+e^{x}}dx=\int \left(\frac{1}{2+e^{x}}\cdot x \right)dx$

If you define $\displaystyle f(x)=\frac{1}{2+e^{x}}$ and $\displaystyle g(x)=x $ then you have:

$\displaystyle \int f(x)g(x) dx$

From here you can simply apply the rule of integration by parts. - May 3rd 2010, 08:22 PMhelpmeee
what is the rule of integration by parts??(Headbang)(Headbang)(Angry)(Bow)

- May 3rd 2010, 08:27 PMCalculusCrazed
Here ya go

Integration by Parts - HMC Calculus Tutorial - May 3rd 2010, 08:34 PMhelpmeee
That made no sense to me.

Please show me with my problem - May 3rd 2010, 08:49 PMlovek323
I don't think integration by parts should be used here.

Are you sure this was the question? This integral is rather difficult to evaluate. Cf. Wolfram Alpha - May 3rd 2010, 08:51 PMDebsta
- May 3rd 2010, 09:01 PMCalculusCrazed
Yeah, because I was trying to do this by parts. It is not easy by any means.

- May 3rd 2010, 09:20 PMmaddas
There's always an integral involving Li(x) on the AP exam, right you guys? The AP board loves those almost as much as Si(x).

- May 3rd 2010, 09:36 PMCalculusCrazed
- May 4th 2010, 04:10 AMmr fantastic
- May 4th 2010, 04:48 AMskeeter