evaluating business investments 2

calculus Evaluating $\int \frac1x^4+1 dx$ Mathematics Stack Exchange

Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. I have an answer to this question(shared Q&A style), but I am curious as to whether there is another way to evaluate the sum. I have been experimenting with double sums for a few weeks now, so many techniques to attack « simple » sums such as this would be much appreciated! Connect and share knowledge within a single location that is structured and easy to search. I would like to answer the question again with an amusing argument . I don’t want the solution, a pointer towards the right way is sufficient.

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• Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
• I don’t want the solution, a pointer towards the right way is sufficient.
• The indefinite integral is a rational fraction and is typically solved using partial fractions decomposition.
• Both the integrals seem to be hard to evaluate and going into some polylogarithmic forms.
• I have an answer to this question(shared Q&A style), but I am curious as to whether there is another way to evaluate the sum.

Please try not to evaluate using any expansion series, unless it’s absolutely impossible to solve the limit without using it. While the last link looks promising, I don’t believe that it answers my specific question(but I haven’t read the paper fully, only skimmed). Luckily, the first integral can be evaluated from here but the second evaluating business investments integral was the dead-end. Both the integrals seem to be hard to evaluate and going into some polylogarithmic forms.

• Connect and share knowledge within a single location that is structured and easy to search.
• Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
• Please try not to evaluate using any expansion series, unless it’s absolutely impossible to solve the limit without using it.
• I don’t want the solution, a pointer towards the right way is sufficient.
• I would like to answer the question again with an amusing argument .

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The indefinite integral is a rational fraction and is typically solved using partial fractions decomposition.