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Top Questions
9
votes
When does the infinite recursive fraction integral $\int_a^b \frac{g(x_1)dx_1}{\int_a^{x_1}\frac{g(x_2)dx_2}{\int_a^{x_2}\cdots}}$ converge?
integration
sequences-and-series
limits
definite-integrals
asked Jul 17, 2023 at 3:56
math.stackexchange.com
7
votes
Solving $\int_1^2 e^{1-\frac{1}{(x-1)^2}} + 2 + \frac{1}{\sqrt{1-\log(x-1)}}\:dx$ with a clean trick
calculus
integration
definite-integrals
improper-integrals
asked Dec 30, 2019 at 6:54
math.stackexchange.com
Top Answers
52
Why is integration by parts not working on this problem?
math.stackexchange.com
33
How to straighten a parabola?
math.stackexchange.com
17
Implicit function equation $f(x) + \log(f(x)) = x$
math.stackexchange.com
17
$\int_ {0}^{\infty} \frac{(e^{3x}-e^x)dx}{x(e^x+1)(e^{3x}+1)}$
math.stackexchange.com
17
How do I evaluate $\lim_{n\to\infty} \,\sum_{k=1}^n\left(\frac{k}{n^2}\right)^{\frac{k}{n^2}+1}$?
math.stackexchange.com
16
How do I evaluate $\int \frac{x+1}{(x^2+1) \sqrt{x^2-6x+1}} dx$?
math.stackexchange.com
15
If $f(x)$ is smooth and odd, must $f(x)/x$ be smooth?
math.stackexchange.com
15
Complex integration tricks for evaluating real integrals
math.stackexchange.com
14
Can anyone help with seeing if this integral definition can be algebraically proven?
math.stackexchange.com
14
Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$
math.stackexchange.com
13
Contour integration with infinite poles
math.stackexchange.com
13
Find the value of $\lim_{n\rightarrow\infty}\int_{-\infty}^{\infty}e^{-x^{2n}}\:\:dx$
math.stackexchange.com
13
Evaluate the indefinite integral $\int \frac{\sin^3\frac\theta 2}{\cos\frac\theta2 \sqrt{\cos^3\theta + \cos^2\theta + \cos\theta}} d\theta$
math.stackexchange.com
12
How to evaluate $\int_0^{\frac{\pi}{2}} \frac{\ln(\cos(x))}{1+\sin^2(x)} \, dx$
math.stackexchange.com
12
Can I get from $\frac{d^2 x}{dt^2} = g$ to $\iint d^2 x = \iint g\,dt^2$?
math.stackexchange.com
12
integral of delta function of x^2
math.stackexchange.com
11
Solve $\Bigl(2 \sin(x)D^2+2 (\cos(x)+\sin(x))D\Bigr)y+2y\cos(x)=\cos(x)$
math.stackexchange.com
11
Solution to $u''(x)-V(x)u(x) = 0$ is identically zero
math.stackexchange.com
11
How do I solve $\int \frac{dx}{\sin^4(x)}$?
math.stackexchange.com
11
Showing that $\lim_{x\to\infty}x^{2}e^{-x^{8}\sin^{2}(x)}$ does not exist.
math.stackexchange.com
11
Numerically evaluating $\iiint_{C} \frac{ {\rm d}x \, {\rm d}y \, {\rm d}z}{x^2 +y^2 + z^2}$
math.stackexchange.com
10
An integral with square root and fractional powers
math.stackexchange.com
10
Compute $\int_{0}^{\infty} \left( \cos\frac{1}{x}+x\sin\frac{1}{x}-2 \right)dx$
math.stackexchange.com
10
Conjecture: $\,\lim\limits_{n\to\infty}\int_0^1 (1+|\sin{nx}|)^{-2}\mathrm dx=\frac{4}{3\pi}$
math.stackexchange.com
10
Find $\cos(\pi^4)$
math.stackexchange.com
10
An Integration of Gamma Function
math.stackexchange.com
10
Finding the Center of Mass of a disk when a part of it is cut out.
math.stackexchange.com
9
Evaluating $\iint\limits_{0\le x\le y\le1}\!\sqrt{1+x^2-y^2}\,{\rm d}x\,{\rm d}y$
math.stackexchange.com
9
Solving $\lim_{n\to\infty}\sqrt n\int_0^{\frac12}(1-3x^2+x^4)^n\mathrm{d}x$
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9
How to evaluate $\int\sqrt{\frac{5+x}{7+x}}dx$?
math.stackexchange.com
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