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51 votes

What is the difference between an indefinite integral and an antiderivative?

calculus terminology asked Nov 29, 2013 at 21:11
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38 votes

Integrate $\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$

calculus integration trigonometry definite-integrals asked Dec 13, 2013 at 17:24
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37 votes

The set of real numbers and power set of the natural numbers

real-analysis elementary-set-theory asked Nov 5, 2013 at 22:42
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29 votes

What does a straight line connecting notes on different clefs mean?

piano notation asked Feb 16, 2016 at 20:38
music.stackexchange.com

28 votes

Fibonacci numbers that are powers of 2

elementary-number-theory asked May 15, 2014 at 10:56
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27 votes

Prove $\int_{0}^\infty \frac{1}{\Gamma(x)}\, \mathrm{d}x = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, \mathrm{d}x$

calculus definite-integrals gamma-function asked Apr 5, 2014 at 16:28
math.stackexchange.com

18 votes

Evaluating $\int_0^\infty \frac {\cos {\pi x}} {e^{2\pi \sqrt x} - 1} \mathrm d x$

calculus integration definite-integrals improper-integrals asked May 18, 2014 at 15:21
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18 votes

Infinite sets with cardinality less than the natural numbers

elementary-set-theory cardinals asked Oct 30, 2013 at 7:58
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17 votes

Proof that one large number is larger than another large number

elementary-number-theory asked Nov 1, 2013 at 14:57
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17 votes

Thank thou or Thank thee

politeness case early-modern-english shakespeare asked Nov 2, 2015 at 21:02
english.stackexchange.com

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Top Answers
88
Why is $(2+\sqrt{3})^{50}$ so close to an integer?
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80
Rules for Product and Summation Notation
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30
When written in decimal notation, every square number has at most 1000 digits that are not 0 or 1. True or false?
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20
Find the Area of the ellipse
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16
Why can't you square both sides of an equation?
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15
Why $\sum_{k=1}^{\infty} \frac{k}{2^k} = 2$?
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12
I need help finding integral of $\frac{1}{x^2+x^4}$
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12
Interesting but short math papers?
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11
Which is greater, $e^{\pi}$ or $\pi^e$?
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10
How to determine countability of $\Bbb N \times \Bbb N \times \Bbb N$?
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9
Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
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9
Formula for Combinations With Replacement
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8
Evaluate $\int_0^e{W(x)}\,\mathrm{d}x$
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7
Infinite Product $\prod\limits_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$
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6
Cantor's Theorem for $\Bbb N$.
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6
Proof by induction that fibonacci sequence are coprime
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6
Proof of divergence of $1/2 + 1/3 + 1/5 + 1/7 + 1/11 +....$
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6
Does $\sum _{ n=1 }^{ \infty }{ \frac { 1 }{ n } } $ diverge?
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6
Double Angle Formula?
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5
Prove that $3\mid n^3 +n$ for all positive integers $n$
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5
Evaluate the integral: $\int\tan^5 (4x)\,\mathrm dx$.
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5
Integrate $\int \frac{\sin^2(x)}{1+\sin^2(x)}dx$
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