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I'm interested in whether or not integrals of the form $I=\int (f(x)/(1+f(x)))\;dx$ exist. In particular, I've been working on polinoms without aby result. Could someone show me how to solve this integral?

$$\int_a^b \frac{f(x)}{1+f(x)} \,dx$$

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    The fact that the function to integrate is $g=f/(1+f)$ is no restriction (except that $g(x)\ne1$ for every $x$) as the inversion $f=g/(1-g)$ shows, hence a **general** result is doubtful. Are you interested in a special class of functions $f$?2012-06-17
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    If $f(x)$ is a polynomial of degree $n$ then $f(x)+1$ will also be. In small cases, one can divide and use $\log$s and $\tan^{-1}$ (maybe up to $\deg 4$), but then things get messy.2012-06-17

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