id
int64 -30,985
55.9k
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-28,785 |
\int z \cdot z\,dz = \frac{1}{2 + 1} \cdot z^{2 + 1} + C = z^3/3 + C
|
-2,257 |
\frac{1}{18} \cdot 5 - \frac{3}{18} = \tfrac{1}{18} \cdot 2
|
-710 |
e^{13*i*\pi*23/12} = (e^{\frac{i*\pi*23}{12}})^{13}
|
-7,989 |
\tfrac{1}{32}(-64 + 96 i + 64 i + 96) = \frac{1}{32}(32 + 160 i) = 1 + 5i
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20,312 |
{(-1) + m \choose l + \left(-1\right)}\cdot \dfrac{1}{l}\cdot m = {m \choose l}
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33,210 |
\tfrac{1}{t} = \dfrac{1}{t}
|
21,734 |
\cos\left(\pi - \operatorname{acos}(q)\right) = -\cos\left(\operatorname{acos}\left(q\right)\right) = -q
|
17,103 |
\left(x C'/x\right)^3 = C'^3 x/x
|
-1,160 |
7/8\cdot (-\tfrac37) = \frac{1}{\frac17\cdot 8}\cdot (1/7\cdot (-3))
|
10,424 |
(-1)^{(3 + \left(-1\right))/2} = \left(-1\right)^1 = -1\Longrightarrow -1
|
30,788 |
e^x =1+x+x^2/2+....
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-18,547 |
-\dfrac{2}{16} = -\frac{1}{8}
|
24,796 |
1/\left(x W\right) = \dfrac{1}{x W}
|
31,869 |
\dfrac{6}{2} \cdot 1 = 3
|
27,109 |
0^2 + (1^2 + 2 \times 2)^2 = 0 + \left(1 + 4\right) \times \left(1 + 4\right) = 0 + 5 \times 5 = 0 + 25 = 25
|
12,233 |
0 = 1 + 1 + 2\cdot (-1) + 3 + 4\cdot (-1) + 5 + 6\cdot \left(-1\right) + 5 + 4\cdot (-1) + 3 + 2\cdot (-1)
|
2,440 |
0 = \|f\|_1\Longrightarrow 0 = f
|
22,256 |
1/(\sqrt{2}) = \frac{1}{\sqrt{2}*2} + \tfrac{1}{\sqrt{2}*2}
|
13,470 |
(-1) + \tan{\pi/2} = 1 + \tan{\pi/2}
|
21,810 |
z^2 = 6 + (6 + (6 + (6 + \ldots)^{1 / 2})^{1 / 2})^{\dfrac{1}{2}} = 6 + z
|
6,855 |
p^8 + (-1) = (p^4 + 1)\cdot (p^4 + \left(-1\right)) = (p^4 + 1)\cdot (p^2 + 1)\cdot \left(p + 1\right)\cdot (p + (-1))
|
10,056 |
(3\times n + 3\times (-1))/3 + \frac{1}{3}\times (3\times n^2 + 3\times n + 1) = (3\times n^2 + 6\times n + 2\times \left(-1\right))/3 = n^2 + 2\times n - 2/3
|
9,546 |
(Z + 0) \cdot Z = Z \cdot Z
|
3,292 |
g^2 + a^2 = (-\left(2\cdot a\cdot g\right)^{1/2} + a + g)\cdot ((g\cdot a\cdot 2)^{\dfrac12} + a + g)
|
-2,505 |
-28^{1/2} + 63^{1/2} = (9*7)^{1/2} - (4*7)^{1/2}
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-5,817 |
\frac{4}{(s + 10)\cdot (6\cdot (-1) + s)} = \dfrac{4}{s^2 + 4\cdot s + 60\cdot (-1)}
|
21,065 |
W^n \cdot W^m = W^{n + m}
|
28,843 |
\cos(-x + \dfrac{\pi}{2}) = \sin\left(x\right)
|
26,180 |
r^2 = \cos{\theta*2}*g^2 rightarrow r*\frac{\mathrm{d}r}{\mathrm{d}\theta} = -\sin{\theta*2}*g^2
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17,957 |
3 + w^3 + 3 w = \left(w + 2\right) \left(w^2 - w\cdot 2 + 7\right) + 11 (-1)
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25,230 |
(1 - 2)^2 + (0 + 1) (0 + 1) - (-2 + 0 + 3)*0*2 = 2
|
-8,978 |
104.7\% = \frac{1}{100}\cdot 104.7
|
-2,444 |
9*\sqrt{7} = \sqrt{7}*(2 + 3 + 4)
|
10,780 |
1 + \dfrac1k = \frac{1}{-\frac{1}{k + 1} + 1}
|
763 |
t + 2 \geq 0 \implies -2 \leq t
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-23,104 |
--\frac{1}{3}4*3 = 4
|
1,399 |
\dfrac{-Z_1 \cdot C + 1.1 \cdot Z_2 \cdot Z_1}{Z_2 \cdot Z_1 \cdot 1.1} = -\frac{C \cdot Z_1}{Z_1 \cdot Z_2 \cdot 1.1} + 1
|
40,103 |
\dfrac{1}{\sqrt{b}} = \dfrac{\sqrt{b}}{\sqrt{b} \cdot \sqrt{b}} = \dfrac{1}{b}\sqrt{b}
|
9,075 |
\cos{\frac{2 π}{5}}*2 + 2 \cos{\tfrac{π}{5} 4} + 1 = 0
|
21,252 |
\sin^2{x} + 1 - \cos^2{\alpha} = \sin^2{\alpha} + 1 - \cos^2{x}
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-9,267 |
30 \cdot g \cdot g - g \cdot 27 = g \cdot 2 \cdot 3 \cdot 5 \cdot g - g \cdot 3 \cdot 3 \cdot 3
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28,424 |
0 \lt 1 + l \implies l > -1
|
20,156 |
w_z + e*w_y = 0 = ( 1, e)*( w_z, w_y)
|
16,110 |
\pi\cdot 2/4 = \dfrac12\cdot \pi
|
16,939 |
2\times \cos(\frac{\vartheta}{2}) = \frac{1}{\sin\left(\vartheta/2\right)}\times \sin(\vartheta)
|
38,309 |
-2 \cdot 5 \cdot 4+ 4 \cdot \binom{5}{2} \cdot \binom{3}{2}+1=81
|
13,000 |
(-1) + p^2 = (1 + p)\cdot (p + (-1))
|
31 |
0.025 = \frac{1}{2}0.05
|
38,883 |
3^2 \cdot 3\cdot 1^{500} = 3^3 = 2\cdot 10 + 7
|
17,280 |
((-1)^4)^{\frac12} = (-1) \cdot (-1) = ((-1)^{1/2})^4
|
3,532 |
\frac{1}{2} (5 + z) (7 (-1) + 2 z) = -\frac{1}{2} 35 + z^2 + z \frac32
|
29,418 |
k = \frac1k \Rightarrow |k| = 2
|
50,041 |
2\cdot 7\cdot 19 = 266
|
18,357 |
(19 - 12 \cdot \sqrt{2}) \cdot (19 + 12 \cdot \sqrt{2}) = 73
|
20,599 |
\frac{c}{c + b} = \frac{1}{c + b}\cdot (c + b) + \dfrac{1}{c + b}\cdot ((-1)\cdot b) = 1 - \frac{b}{c + b}
|
19,990 |
0\cdot 5! + 4\cdot 4! + 0\cdot 3! + 0\cdot 2! + 1!\cdot 0 + 0! = 97
|
1,912 |
{l \choose s} = \frac{l!}{(l - s)!\cdot s!}
|
-9,702 |
0.7 = \frac{1}{20}14
|
-2,777 |
\sqrt{10}*(2 + 4 + (-1)) = 5\sqrt{10}
|
39,985 |
4! \cdot 5 \cdot 4 \cdot 3 \cdot 2 = 4! \cdot 5!
|
-19,343 |
5/7*\frac17*8 = \frac{8*\frac{1}{7}}{1/5*7}
|
11,016 |
y - \frac{2}{3}*w = 0 \Rightarrow \dfrac{2}{3}*w = y
|
12,542 |
-a V + l_1 = c z \Rightarrow z = \left(l_1 - V a\right)/c
|
15,333 |
t*z*k = k*t*z
|
130 |
(\pi \cdot \left(-1\right) \cdot a^2)/(\sqrt{2}) = -\sqrt{2} \cdot \pi \cdot \frac{a^2}{2}
|
-587 |
(e^{\dfrac{23}{12}\cdot i\cdot \pi})^{16} = e^{16\cdot \frac{i\cdot \pi}{12}\cdot 23}
|
29,779 |
\dfrac59 = \frac{1}{6^2 \cdot 6} \cdot 120
|
26,129 |
1 = \frac1y\cdot (c - x) rightarrow y + x = c
|
10,871 |
\frac56 = \frac{1}{3!} \left((-1) + 3!\right)
|
4,277 |
\frac{1}{2 + (-1)}*(5^{25} + (-1) + 75*(-1)) = 5^{25} + 76*(-1) \gt \frac14*(5^{25} + 101*\left(-1\right))
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-18,957 |
14/15 = \frac{X_q}{25*\pi}*25*\pi = X_q
|
20,413 |
2 + \left(z + 2 \times (-1)\right)^2 = 6 + z^2 - 4 \times z
|
14,918 |
8/15 = \frac{1}{5} + \frac{1}{3}
|
-5,174 |
38.8*10 10 = 10^{1 + 1}*38.8
|
-1,304 |
\frac{7}{6}\cdot (-\dfrac{4}{7}) = \frac{7 / 6}{(-7)\cdot 1/4}\cdot 1
|
16,784 |
\left(I\cdot x + I'\right) \cdot \left(I\cdot x + I'\right) = x\cdot I + I'
|
-20,815 |
\frac{5 - c}{c\cdot 7 + 35\cdot (-1)} = \frac{5\cdot (-1) + c}{c + 5\cdot (-1)}\cdot \left(-\dfrac{1}{7}\right)
|
30,985 |
\frac{\frac{1}{6}}{4!} = \frac{1}{144}
|
-5,251 |
10^{-1 + 6}*5.6 = 5.6*10^5
|
22,967 |
2f - f + (-1) = 1 + f
|
28,972 |
W*W^l = W^{l + 1}
|
3,459 |
(-1) + 3*2^{10} = 3071
|
22,176 |
\frac1q(\xi\cdot (-1)) = -\frac{\xi}{q}
|
6,071 |
2 \cdot m + 2 \cdot (-1) - (-1) + m = (-1) + m
|
14,110 |
\frac{\mathrm{d}}{\mathrm{d}y} (y^2 + 2*y) = 2*y + 2
|
36,733 |
\frac{d^k}{d^n} = d^{k - n}
|
31,820 |
(1 - 5^{1 / 2}) (1 + 5^{\frac{1}{2}}) = -4
|
27,175 |
f = \frac{f}{f} \times f
|
19,790 |
\mathbb{E}(R_1 R_2) = \mathbb{E}(R_1) \mathbb{E}(R_2)
|
-2,653 |
\sqrt{27} + \sqrt{48} + \sqrt{75} = \sqrt{9\cdot 3} + \sqrt{16\cdot 3} + \sqrt{25\cdot 3}
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49,201 |
5*\binom{4}{2} + 4*\binom{5}{2} = 5*6 + 4*10 = 70
|
22,707 |
\tfrac{1 + n}{n + 1 - m} = \frac{1}{-\frac{m}{n + 1} + 1}
|
882 |
G\cdot y = y\cdot G
|
20,984 |
\dfrac{1}{a + b} \times a \times b = a - \frac{a^2}{a + b} = b - \tfrac{b^2}{a + b}
|
23,279 |
x = z + zx \Rightarrow \frac{1}{-z + 1}z = x
|
-17,200 |
\frac{1}{\cos^2{x}}\times (-\sin^2{x} + 1) = \frac{1}{\cos^2{x}}\times \cos^2{x}
|
21,535 |
\sin\left(w\right) \sin(B)\cdot 2 = -\cos(B + w) + \cos(-B + w)
|
995 |
a/c + c/a = (c^2 + a^2)/(a*c)
|
987 |
10 \cdot ((-1) + 10) (2\left(-1\right) + 10) (3(-1) + 10)/4! = 210
|
13,840 |
z^4 + \left(-1\right) = (z^2 + 1)*\left(z^2 + (-1)\right) = (z + i)*\left(z - i\right)*\left(z + 1\right)*(z + \left(-1\right))
|
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