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Bookmark or Share- Easy way to compute logarithms without a calculator?I would need to be able to compute logarithms without using a calculator, just on paper. The result should be a fraction so it is the most accurate. For example I have seen this in math class calc...
- Evaluating $ \\lim\\limits_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n ...Here's another approach. First, note that $$\begin{eqnarray*} \sum_{k=n^2+1}^\infty \frac{n}{n^2+k^2} &
- calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...I am trying to evaluate the integral $$\int \frac{1}{1+x^4} \mathrm dx.$$ The integrand $\frac{1}{1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I ...
- integration - Evaluating $\int_0^2(\tan^{-1}(\pi x)-\tan^{-1} x ...Hint given: Write the integrand as an integral. I'm supposed to do this as double integration. My attempt: $$\\int_0^2 [\\tan^{-1}y]^{\\pi x}_{x}$$ $$= \\int_0^2 ...
- Evaluating $\\int_0^{\\infty}\\frac{\\ln(x^2+1)}{x^2+1}dx$$\begingroup$ @Ron You directed me to your post, so I hope you're willing to answer some of my questions. I don't think the branch of $\log(1+z^{2})$ you used coincides with that cut.
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