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 + x 4. Any other methods are also wellcome.
algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
When I tried to solve this problem, I found a solution (official) video on YouTube. That is a = −b, c = 2024 a = b, c = 2024 and the correct answer is 1 20242025 1 2024 2025. Is there an alternative solution but not using (a + b)(a + c)(b + c) + abc = (a + b + c)(ab + ac + bc) (a + b) (a + c) (b + c) + a b c = (a + b + c) (a b + a c + b c) ?
Evaluating $\\lim_{n\\to\\infty}\\left( \\frac{\\cos\\frac{\\pi}{2n ...
Jan 24, 2025 · The problem is to solve: $$\lim_ {n\to\infty}\left ( \frac {\cos\frac {\pi} {2n}} {n+1}+\frac {\cos\frac {2\pi} {2n}} {n+1/2}+\dots+\frac {\cos\frac {n\pi} {2n}} {n+1 ...
Evaluating $ \\lim\\limits_{n\\to\\infty} \\sum_{k=1}^{n^2} …
How would you evaluate the following series? $$\\lim_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n^2+k^2} $$ Thanks.
calculus - Evaluating $\int e^ {x\sin x+\cos x}\left (\frac {x^4\cos^3 ...
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Evaluating $\\int_0^1 (1-x^2)^n dx$ - Mathematics Stack Exchange
Mar 15, 2021 · Evaluating ∫1 0 (1 − x2)ndx ∫ 0 1 (1 x 2) n d x [duplicate] Ask Question Asked 4 years, 4 months ago Modified 4 years, 4 months ago
Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1/2x}}{x} $ without ...
Sep 11, 2024 · Evaluating limx→0 e−(1+2x)1/2x x lim x → 0 e (1 + 2 x) 1 / 2 x x without using any expansion series [closed] Ask Question Asked 10 months ago Modified 10 months ago
Evaluating $\\int_0^{\\infty}\\frac{\\ln(x^2+1)}{x^2+1}dx$
How would I go about evaluating this integral? $$\int_0^ {\infty}\frac {\ln (x^2+1)} {x^2+1}dx.$$ What I've tried so far: I tried a semicircular integral in the positive imaginary part of the complex p...
Evaluating $\\lim\\limits_{R\\to +∞}\\iint_{x^2+y^2\\leq R^2}\\left ...
Dec 20, 2021 · I wonder whether you would agree that the second line above is easier to read than the first. Note (1) the use of \left and \right, which makes the parentheses assume appropriate sizes, (2) the use of \limits, which affects the position of the bounds of integration, and (3) small spaces separating dx d x and dy d y from what precedes and follows them.
Evaluating $ \\frac{35887+j(1050)}{-2824+j(-17)}$, where $j^2=-1$
$$ \frac {35887+j (1050)} {-2824+j (-17)} \ = \ ? $$ This above number is supposed to be the sprung mass response factor to road input at frequency of 6.91 radians/second for the front suspension of a