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ddrg
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math_formulas

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int64
-30,985
55.9k
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32,702
0 = -2^0 + 3^0
-10,468
10/10*\left(-\frac{6}{5 + 5*k}\right) = -\dfrac{1}{50*k + 50}*60
16,055
\int 1 \cdot 2 \cdot \pi \cdot x\,dx = 2 \cdot \pi \cdot \frac{x^2}{2} = \pi \cdot x^2
52,877
\frac{{40 \choose 3}}{{52 \choose 3}} \cdot {12 \choose 0} = \dfrac{{40 \choose 3}}{{52 \choose 3}}
12,021
1 + \sin{2 x} = t^2 \Rightarrow \sin{2 x} = t^2 + (-1)
2,799
20/132 = 5/12\cdot 4/11
-19,716
70/8 = \dfrac{7*10}{8}
13,171
\left((-1) + n\right) (n + 1) = n^2 + (-1)
25,389
1/3 + 1/3 + \frac{1}{3} = 1
11,407
i + 3\cdot (-i\cdot 7) = -i\cdot 20
2,852
y^2 + 5*y + 2 = (y + 2)^2 = y^2 + 4*y + 4 rightarrow y = 2
-18,383
\frac{1}{16 + x \cdot x - 8\cdot x}\cdot (x^2 - 4\cdot x) = \dfrac{x\cdot (x + 4\cdot \left(-1\right))}{(x + 4\cdot (-1))\cdot (x + 4\cdot (-1))}
19,553
\sin(-\pi \cdot y) \cdot \left(-y\right) = y \cdot \sin(y \cdot \pi)
7,711
a = 2\cdot x^2 - 5\cdot x + 2\cdot (-1) \Rightarrow x^2\cdot 2 - 5\cdot x + 2\cdot (-1) - a = 0
21,506
n + 2 \times (-1) + (3 \times \left(-1\right) + n) \times 2 + (4 \times (-1) + n) \times (3 \times (-1) + n) = \left(2 \times (-1) + n\right)^2
14,178
\dfrac{d_2}{d_1} = d_1 \cdot d_2 = d_2 \cdot d_1 = \frac{1}{d_1} \cdot d_2
-9,441
40 \cdot y = 2 \cdot 2 \cdot 2 \cdot 5 \cdot y
-16,816
-7 = -7 \cdot \left(-2 \cdot t\right) - -56 = 14 \cdot t + 56 = 14 \cdot t + 56
-22,431
64^{\dfrac{2}{3}} = (64^{1/3})^2 = 4 * 4 = 4*4 = 16
-4,490
\dfrac{5}{y + 3} - \frac{4}{y + (-1)} = \frac{y + 17 \cdot (-1)}{3 \cdot (-1) + y^2 + y \cdot 2}
48,017
\frac{1}{(v - y)^2} = \frac{\partial}{\partial v} \frac{1}{v - y} = \dfrac{1}{y^2} + \dfrac{1}{y^3}*2*v + \frac{3*v^2}{y^4}
-17,676
11 \cdot \left(-1\right) + 34 = 23
4,923
(1 - \cos{\tau})/\sin{\tau} = \frac{2 \cdot \sin^2{\tfrac{\tau}{2}}}{2 \cdot \sin{\tau/2} \cdot \cos{\tau/2}} = \tan{\tau/2}
11,993
(h + a)^2 = a^2 + h^2 + a\cdot h\cdot 2
6,338
\frac{1}{2\cdot 2} + \frac{1}{2} = \frac{3}{4}
24,929
Z_q = \frac{\partial}{\partial q} Z_q
38,607
\frac{1}{-d + 1} = 1 + d + d^2 + d^2 \cdot d + d^4 + \dots
20,523
\frac{7}{4}\cdot \pi = \tfrac{3\cdot \pi}{2}\cdot 1 + \pi/4
-9,861
-\dfrac{1}{100} 47 = 0.01 \left(-47\right)
-22,710
28/49 = 4*7/(7*7)
-22,211
(x + 3) \cdot (x + 7) = 21 + x^2 + 10 \cdot x
24,733
z^4 + 1 = z^4 + 2 z z + 1 - 2 z^2
13,024
1/4 + 3*3/4 = 2.5
-15,523
\dfrac{(\frac{1}{x})^5}{\frac{1}{\frac{1}{r^4} \cdot \frac{1}{x^4}}} = \frac{1}{x^5 \cdot r^4 \cdot x^4}
13,220
\left(4 < 17^{1 / 2} \implies -1 - 17^{1 / 2} < -5\right) \implies -1 > \left(-17^{\dfrac{1}{2}} - 1\right)/4
17,069
p^2 \cdot 3 = p^2 + 2 \cdot p \cdot p
-18,504
-\frac{1}{28} \cdot 53 = -53/28
-26,056
-h^2 + d^2 = (d - h) \cdot (d + h)
11,868
-\pi\cdot (-4) - 2\cdot \pi = 2\cdot \pi
-26,671
\left(z + 3\right)\cdot (3\cdot (-1) - z\cdot 7) = -7\cdot z^2 - z\cdot 24 + 9\cdot (-1)
-11,921
1.47\cdot 0.001 = \tfrac{1.47}{1000}
2,005
\cos{x} = \left(e^{i x} + e^{-i x}\right)/2 = \cosh{i x}
30,259
\sqrt{A \cdot Z} = Z rightarrow Z = 0\text{ or }A = Z
-15,843
\frac{5}{10} - 5\cdot \dfrac{9}{10} = -\frac{1}{10}\cdot 40
13,599
((-1) + d) \cdot ((-1) + d) = 1 + d \cdot d - d\cdot 2
41,896
\frac{1}{3 + v^2 + v} = \frac{1}{3 + v^2 + v}
-22,388
1 + 3\cdot (-1) = -2
17,811
k + 1 + (1 + k \cdot k \cdot k + 3\cdot k^2 + k\cdot 3)\cdot 2 = 2\cdot k^3 + k + 3\cdot \left(2\cdot k^2 + k\cdot 2 + 1\right)
14,632
\left|{A \cdot Z}\right| = \left|{A \cdot Z}\right|
26,163
15\cdot 200 = 3000
-7,728
(-5 + 5\cdot i)/5 = -5/5 + \frac55\cdot i
-21,043
6/12 = \dfrac133\cdot 2/4
23,082
x \cdot 2 = x + \sqrt{-2} + x - \sqrt{-2}
23,626
2000 = (60\cdot (-1) + 90)^2 + (60\cdot (-1) + 30)^2 + (50 + 60\cdot \left(-1\right))^2 + \left(60\cdot (-1) + 70\right)^2
6,891
(H \cdot H^Q)^Q = (H^Q)^Q \cdot H^Q = H \cdot H^Q
-1,611
7/6 \pi + \frac{1}{12}17 \pi = \pi\cdot 31/12
-20,741
\tfrac{x + 8 \cdot (-1)}{8 \cdot (-1) + x} \cdot (-3/1) = \frac{1}{8 \cdot (-1) + x} \cdot (-3 \cdot x + 24)
13,348
(g + b + 4\cdot h) \cdot (g + b + 4\cdot h) + (g + b)^2 = (b + g)^2 + (g + 2\cdot h + b + h\cdot 2)^2
-1,714
\frac{5}{6} \cdot \pi = -5/12 \cdot \pi + 5/4 \cdot \pi
9,926
\sin^4\left(x\right) \cdot \cos^2(x) = \sin^4(x) \cdot (1 - \sin^2(x)) = \sin^4(x) - \sin^6(x)
32,915
x^n + (-1) = \left(x + (-1)\right) \cdot (x^{n + (-1)} + x^{n + 2 \cdot (-1)} + \cdots + x + 1)
-22,173
\frac{1}{18} \cdot 24 = \tfrac{4}{3}
20,892
1 + 2^{555} + 5\cdot 2^{444} + 10\cdot 2^{333} + 10\cdot 2^{222} + 5\cdot 2^{111} = \left(1 + 2^{111}\right)^5
35,876
3/1 = 3 \cdot (-1) + x rightarrow 6 = x
-19,738
35/8 = \frac{1}{8}35
2,689
2\cdot \frac{1}{8}\cdot 1 / 64 = \dfrac{2}{512}
-13,437
\frac{1}{8 + 6\times (-1)}\times 10 = 10/2 = \dfrac{10}{2} = 5
31,856
(g + b)^n = g + b = g^n + b^n
22,472
\sum_{i=1}^k i^3 = (\sum_{i=1}^k i)^2
304
2 = 49\cdot y^2 + 3\cdot y^2 + 9\cdot y^2 + (-7\cdot y + y + 3\cdot y)^2 = 70\cdot y \cdot y
54,838
0 = \tfrac{1}{\infty}
19,154
\frac{36 + 4}{36 + 4 + 3 + 3} = \frac{1}{46} \cdot 40 = \tfrac{20}{23}
-19,804
-0.35 = -\dfrac{1}{40} \cdot 14
22,225
2 \cdot 6 + 2 \cdot 8 = 28
13,873
e^{\frac{1}{x}} = 1 + 1/x + \frac{1}{2 \cdot x \cdot x} + ... \gt \frac{1}{2 \cdot x^2}
52,729
104 = 34\times 3 + 2
26,199
\frac{j^2}{j + y} = j - y + \frac{y^2}{j + y}
-5,038
4.68 \cdot 10 = \dfrac{4.68}{1000} \cdot 10 = 4.68/100
2,746
\dfrac{2}{n} + (-1) \leq -1 rightarrow 2/n \leq 0
19,883
\mathbb{E}[Y_1\cdot Y_2^2] = \mathbb{E}[Y_1]\cdot \mathbb{E}[Y_2 \cdot Y_2]
10,873
9/25 = \frac{3}{5}\cdot \dfrac35
5,963
x^3\cdot N = 8^3 \Rightarrow 8\cdot 8 \cdot 8 = N\cdot x^2\cdot x
-20,580
\frac{1}{2 n + 2 \left(-1\right)} (n + 3 (-1))*5/5 = \frac{1}{n*10 + 10 (-1)} (5 n + 15 (-1))
30,613
2^{i + 1} + 2(-1) = 2^1\cdot 2^i + 2(-1) = 2\cdot (2^i + \left(-1\right))
-13,453
\frac{1}{3 + (-1)} \cdot 6 = 6/2 = \frac{6}{2} = 3
21,750
\left(\alpha + (-1)\right) \cdot \left(\alpha + 1\right) = (-1) + \alpha^2
-22,366
k^2 - k \cdot 3 + 18 \cdot (-1) = \left(3 + k\right) \cdot (k + 6 \cdot \left(-1\right))
5,361
2 = 2 + 0\cdot 7
21,250
-d \cdot 16 + a^2 \cdot 4 + 4d^2 + 64 - 4da - 16 a = (-d + a)^2 \cdot 3 + \left(8(-1) + a + d\right)^2
8,768
-(1 + 6*n_2) + 6*n_1 + 1 = 2*(n_1*3 - n_2*3)
-17,753
52\times (-1) + 79 = 27
7,629
\left(-1\right) + x = \frac12\cdot (x + (-1)) + ((-1) + x)/2
1,409
-n^{1/2} + (n + 1)^{1/2} = \frac{1}{(n + 1)^{1/2} + n^{1/2}}
-25,717
\frac{\mathrm{d}}{\mathrm{d}t} \left(3 \times e^{2 \times t}\right) = 2 \times 3 \times e^{2 \times t} = 6 \times e^{2 \times t}
15,832
(b + (-1)) (b^2 + b + 1) = b^3 + (-1)
-20,223
\frac{72}{72\cdot \left(-1\right) - 45\cdot x} = \dfrac{9}{9}\cdot \frac{8}{-x\cdot 5 + 8\cdot (-1)}
-3,726
\tfrac{40\cdot q^5}{5\cdot q^4} = \frac{q^5}{q^4}\cdot 40/5
16,251
(z^3 + \eta * \eta * \eta)*(\eta^6 - z^3*\eta * \eta^2 + z^6) = z^9 + \eta^9
43,921
4^n = 2^n*2^n \geq (1 + n)^2
19,657
\mathbb{N} = \left\{\dots, 4, 2, 3, 0, 1\right\}