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calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
The integrand 1 1+x4 1 1 + x 4 is a rational function (quotient of two polynomials), so I could solve the integral if I can find the partial fraction of 1 1+x4 1 1 + x 4. But I failed to factorize 1 +x4 1 + …
Evaluating integrals with sigma notation - Mathematics Stack …
Evaluating integrals with sigma notation Ask Question Asked 13 years, 2 months ago Modified 8 years, 2 months ago
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? ∫∞ 0 log(1 + x) 1 + x2 dx = π 4log2 + Catalan constant
integration - Evaluating $\int_ {0}^ {2\pi}\cos ^2 (x)\sin (x) \ dx ...
Jun 3, 2024 · Evaluating ∫2π 0 cos2(x) sin(x) dx ∫ 0 2 π cos 2 (x) sin (x) d x Ask Question Asked 1 year, 1 month ago Modified 1 year, 1 month ago
Evaluating $\\sqrt{119^2+120^2}$ with clever algebra
Sep 13, 2022 · Numbers $(119,120,169)$ are Pythagorean triples, i.e $119^2+120^2=169^2$. I'm wondering is it possible to start from $119^2+120^2$ and get $169^2$ algebraically without …
complex numbers - Evaluating $\cos (i)$ - Mathematics Stack …
Nov 27, 2020 · Others answered about how cos(i) c o s (i) can be calculated using Euler's formula. But I will elaborate from a different perspective. We know that cosine function can be …
complex numbers - Evaluating $2^i$ - Mathematics Stack Exchange
It is obvious that we should use Euler's formula, but the fact that $\\Vert e^{i \\alpha} \\Vert = 1$ (while the base is 2) brings difficulty of using it. Can anyone think of a way evaluate this. Tha...
integration - Evaluating $\int x^2 \sqrt {x^2-1} dx$ - Mathematics ...
2 How do I evaluate the following indefinite integral? As a general rule, whenever evaluating an integral containing x2 ±a2− −−−−−√ x 2 ± a 2, one of the most natural substitutions is x = a …
Evaluating $\\lim\\limits_{x\\to-3}\\frac{x^2-9}{2x^2+7x+3}$
The important thing to know at this level of evaluating limits is that if the numerator is zero, you can only conclude the whole thing is zero if the denominator is not zero. We sometimes say 0 …
algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
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