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 …

I am suppose to use Theorem 4 in my books (just the limit as n approaches infinity of a summation representing the function). I am trying to evaluate $$ \\int_2^5 (4-2x) dx$$ I really …

In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a …

I'm supposed to calculate: $$\\lim_{n\\to\\infty} e^{-n} \\sum_{k=0}^{n} \\frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\\frac{1}{2 ...

Here's another approach. First, note that $$\begin{eqnarray*} \sum_{k=n^2+1}^\infty \frac{n}{n^2+k^2} &<& \sum_{k=n^2+1}^\infty \frac{n}{k^2} \\ &\le& n\int_{n^2 ...

Feb 14, 2016 · 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 …

Oct 20, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Jul 7, 2015 · I agree entirely with the accepted answers; that is how the integral should be attempted analytically. However, if you wish to compute integrals of this form over the unit …

Jan 17, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

While working on some probability question, I had to evaluate $\lim_{x \to \infty} \arctan(x)$. I knew the answer intuitively as $\pi/2$, yet I cannot figure out how to prove it by elementary …