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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algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
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Evaluating $e^ {\log_ {e} 2^ {16}}$ using exponential and log ...
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Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1/2x}}{x} $ without ...
Sep 11, 2024 · The following is a question from the Joint Entrance Examination (Main) from the 09 April 2024 evening shift: $$ \lim_ {x \to 0} \frac {e - (1 + 2x)^ {1/2x}} {x} $$ is equal to: (A) …
Evaluating $\\int_0^1 (1-x^2)^n dx$ - Mathematics Stack Exchange
Mar 15, 2021 · Evaluating $\int_0^1 (1-x^2)^n dx$ [duplicate] Ask Question Asked 4 years, 6 months ago Modified 4 years, 6 months ago
Easy way to compute logarithms without a calculator?
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 …
Evaluating $\lim_ {n\to\infty}\int_0^n (1- (x/n))^ne^ {x/2}dx$
Jul 21, 2016 · $$ \mbox {How to compute}\quad \lim_ {n \to \infty}\,\,\int_ {0}^ {n}\left (1 - {x \over n}\right)^ {n} \,\mathrm {e}^ {x/2}\,\,\mathrm {d}x\,\,\, ?. $$ No ideas how ...
Evaluating $\lim\limits_ {n\to\infty} e^ {-n} \sum\limits_ {k=0}^ {n ...
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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 …