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 ...
Evaluating $\cos (i)$ - Mathematics Stack Exchange
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Evaluating $\sum_ { (a,b,c)\in T}\frac {2^a} {3^b 5^c}$, for $T$ the ...
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Evaluating $\\int_0^{\\infty}\\frac{\\ln(x^2+1)}{x^2+1}dx$
How would I go about evaluating this integral? $$\int_0^ {\infty}\frac {\ln (x^2+1)} {x^2+1}dx.$$ What I've tried so far: I tried a semicircular integral in the positive imaginary part of the complex p...
Evaluating $e^ {\log_ {e} 2^ {16}}$ using exponential and log ...
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calculus - Evaluating $\int_0^\infty \frac {\log (1+x)} {1+x^2}dx ...
May 19, 2013 · Can this integral be solved with contour integral or by some application of residue theorem? $$\\int_0^\\infty \\frac{\\log (1+x)}{1+x^2}dx = \\frac{\\pi}{4}\\log 2 ...
Evaluating $\lim\limits_ {n\to\infty} e^ {-n} \sum\limits_ {k=0}^ {n ...
I'm supposed to calculate: $$\\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 ...
calculus - Evaluating $\ln (\cos x))$ using Taylor expansion ...
Evaluating $\ln (\cos x))$ using Taylor expansion Ask Question Asked 11 years, 2 months ago Modified 11 years, 2 months ago
Evaluating a Complex Integral involving Bessel Function
Jan 12, 2025 · Evaluating a Complex Integral involving Bessel Function Ask Question Asked 9 months ago Modified 9 months ago
evaluating $\Gamma (1/2)$ using elementary methods
Aug 22, 2021 · evaluating $\Gamma (1/2)$ using elementary methods Ask Question Asked 4 years, 2 months ago Modified 4 years, 2 months ago