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).
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.
Here ya go
Integration by Parts - HMC Calculus Tutorial
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