id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
2,465 | c^x = 1 + x \cdot \log_e(c) + \frac{\log_e(c)^2}{2} \cdot x \cdot x + \frac{x^3}{6} \cdot \log_e(c)^3 \cdot \cdots |
22,791 | C^{\beta + x} = C^x C^\beta |
-20,090 | \dfrac{1}{r + (-1)}\cdot 1 = \frac{1}{5\cdot r + 5\cdot (-1)}\cdot 5 |
294 | \frac{2\cdot x}{x + 2\cdot (-1)}\cdot 1 = \frac{1}{x + 2\cdot \left(-1\right)}\cdot \left(2\cdot x + 4\cdot (-1) + 4\right) = 2 + \dfrac{1}{x + 2\cdot \left(-1\right)}\cdot 4 |
-3,119 | \sqrt{2}*(4 + 3*\left(-1\right) + 2) = \sqrt{2}*3 |
4,608 | -(x + \left(-1\right)) + K = 1 + K - x |
-21,671 | \frac{1}{3}*2 = 2/3 |
-5,972 | \frac{1}{30 + q^2 + 11\cdot q}\cdot q = \frac{q}{(6 + q)\cdot (q + 5)} |
494 | (-y + x) (y^2 + x^2 + xy) = x \cdot x^2 - y^3 |
21,087 | 1 + x + 0(-1) = x + 1 |
-7,079 | 1/12 = \frac38 \cdot 2/9 |
-7,999 | \dfrac{3}{-3i} - \dfrac{12i}{-3i} = \dfrac 1i \left(\dfrac{3}{-3} - \dfrac{12i}{-3} \right)= \dfrac 1i (-1+4i) |
2,807 | \dfrac{1}{1 - z}\cdot (4\cdot z + 3\cdot (-1)) = -\frac{1}{z + (-1)}\cdot (4\cdot (z + (-1)) + 1) = -4 + \frac{1}{1 - z} |
38,800 | \binom{9}{2} - \binom{3}{2} \cdot \binom{3}{1} = 27 |
13,924 | 4*(x + 1)^2 + 1 = 4*x^2 + 8*x + 4 + 1 = 4*x^2 + 1 + 8*x + 4 < 3*2^x + 8*x + 4 |
-18,258 | \frac{x \cdot (x + 6 \cdot (-1))}{(x + 6 \cdot (-1)) \cdot (6 \cdot \left(-1\right) + x)} = \frac{-6 \cdot x + x^2}{x^2 - 12 \cdot x + 36} |
-28,997 | 3 = \frac{1}{2}*\left(3 - -3\right) |
12,110 | \sin(\alpha) \cos(\beta) + \sin\left(\beta\right) \cos(\alpha) = \sin\left(\beta + \alpha\right) |
27,878 | g^k\cdot g^l = g^{l + k} |
29,781 | (y + 1)*(1 + y) = y^2 + y*2 + 1 |
-15,711 | \dfrac{{(p^{5})^{2}}}{{(p^{4}t^{-4})^{-3}}} = \dfrac{{p^{10}}}{{p^{-12}t^{12}}} |
1,674 | (-1) + \sqrt{2} = (2^{1/4} + (-1)) \left(1 + 2^{\frac14}\right) |
22,406 | (u_1 + u_2) dR = u_1 Rd + u_2 Rd |
35,763 | 1 - \frac{\sin(2\cdot x)}{2} = 1 - \sin(x)\cdot \cos(x) = \sin^2(x) + \cos^2\left(x\right) - \sin(x)\cdot \cos\left(x\right) |
14,622 | (c_1 c_2) (c_1 c_2) (c_1 c_2) = 1 = 1 = c_1^3 c_2^3 |
-639 | (e^{\frac{7πi}{6}})^5 = e^{5iπ*7/6} |
-1,792 | \pi \dfrac{1}{12}7 - \frac{1}{12}7 \pi = 0 |
26,478 | p^2 + 2qp + q^2\cdot 2 = q \cdot q + (q + p)^2 |
-26,201 | 5 \cdot 6 - \frac126 = 30 + 3\left(-1\right) = 27 |
34,360 | -p + p^3 + p * p = (-1) + p^2 + p^2 - p + p^2 - p + p^2 - p*2 + 1 + p^3 - p^2*3 + p*3 |
3,571 | 1 + x^4 = 1 + 2x^2 + x^4 - 2x^2 = \left(1 + x^2\right)^2 - (\sqrt{2} x) \cdot (\sqrt{2} x) |
26,102 | a_n + a_{\left(-1\right) + n} + \dots + a_2 + a_1 = a_1 + a_2 + \dots + a_{(-1) + n} + a_n |
3,268 | z - \tfrac{z^3}{3!} + \dfrac{z^5}{5!} - z^7/7! - \cdots = \sin{z} |
10,535 | \frac{n^2}{1 + n^2} = -\frac{1}{n^2 + 1} + 1 |
33,741 | \frac{1}{9}*7 = -\frac{10}{9} + \frac{1}{9}*17 |
5,563 | 6\cdot (-1) + 3\cdot x = x + 2\cdot (x + 3\cdot (-1)) |
-6,745 | 40/100 + \frac{1}{100}*6 = \frac{1}{100}*6 + 4/10 |
143 | r*(y_1 + \lambda*y_0) = r*\lambda*y_0 + r*y_1 |
-7,008 | 3/8\cdot \frac17\cdot 6 = \frac{9}{28} |
45,752 | 2^2\times 11\times 131 = 5764 |
-1,454 | \frac{1}{63} \cdot 72 = \tfrac{8}{63 \cdot \dfrac19} \cdot 1 = \frac{8}{7} |
10,360 | (\sqrt{2} + 2) (11 - 7 \sqrt{2}) = \left(2 - \sqrt{2}\right) \left(5 + \sqrt{2}\right) |
-30,269 | \frac{1}{c + \left(-1\right)}\left(c * c + 2c + 3(-1)\right) = \frac{(c + 3) (c + \left(-1\right))}{c + (-1)} = c + 3 |
-20,247 | 42 q/(q*(-24)) = ((-6) q)/(q*(-6)) (-\dfrac{1}{4}7) |
-1,704 | \frac{11}{6} \pi - \pi*4/3 = \frac{\pi}{2} |
7,707 | -n^2 + \left(n + 1\right)^2 = n \cdot 2 + 1 |
-4,335 | \dfrac{x\times 60}{x^2 \times x\times 50}\times 1 = \frac{x}{x^3}\times 60/50 |
-28,842 | \tfrac{1}{7} - n\cdot 9/7 + 6/7 = 6/7 + \frac17 - n\cdot 9/7 |
-3,056 | \sqrt{175} - \sqrt{28} = -\sqrt{4 \cdot 7} + \sqrt{25 \cdot 7} |
-8,792 | 25 = 1/2*10*5 |
10,637 | E_{i,j} Z = E_{i,j} Z |
38,027 | 48\cdot 16/24 = 32 |
-5,179 | 3.360 \times 10 = {3.360 \times 10} \times 10^{2} = 3.360\times 10^{3} |
23,104 | 1 + 4*r = -7 + 4*\left(r + 2\right) |
29,480 | 9*(-1) + 121 = 112 |
817 | 0 = a + b*x \implies x = -a/b = b*1/2/b = \frac{1}{2} |
43,185 | 8\cdot 2 + 1 = 17 |
2,624 | (\dfrac{z}{-z + 4 \cdot (-1)})^{1/2} = (\frac{(-1) \cdot z}{z + 4})^{1/2} = \frac{\left(-z\right)^{1/2}}{(4 + z)^{1/2}} |
-19,023 | 23/30 = A_s/\left(25\cdot \pi\right)\cdot 25\cdot \pi = A_s |
11,910 | \cos\left(\tfrac{\pi}{2} - w\right) = \sin(w) |
23,487 | 2^g + 3^f = (1 + 1)^g + \left(1 + 2\right)^f \leq 1 + g + 1 + f\cdot 2 |
2,148 | (t^2 + q^2 + t*q)*\left(-t + q\right) = -t^3 + q^3 |
30,308 | 5^{n*2} = (5^n)^2 + 0 * 0 |
558 | \left(1 + y^3 = 0 \Rightarrow -2 = y \cdot y \cdot y + (-1)\right) \Rightarrow -2 = (y + \left(-1\right)) \cdot (1 + y^2 + y) |
17,016 | E[\sum_{k=1}^x Q_k] = \sum_{k=1}^x E[Q_k] |
-19,463 | \frac{9}{5} \cdot 3/4 = \tfrac{3 / 4}{5 \cdot 1/9} \cdot 1 |
25,441 | \mathbb{E}\left(Z_1\right) \mathbb{E}\left(Z_2\right) = \mathbb{E}\left(Z_1 \mathbb{E}\left(Z_2\right)\right) |
30,726 | 2x^2 + 3x + 1 = (2x + 1) (1 + x) |
15,176 | z_x = x*2 f' y \implies y^2 z_x = x f' y y y*2 |
3,899 | (2*\sqrt{2} + 5)*\left(5 - 2*\sqrt{2}\right) = 17 |
43,262 | \left\lceil{\tfrac{6*75}{100}}\right\rceil = 5 |
11,140 | x^2 + z^2 = 0.5\cdot \left(\left(x - z\right) \cdot \left(x - z\right) + \left(x + z\right)^2\right) |
22,680 | 1 + 27 - 2\cdot 8 = 12 |
-15,298 | \dfrac{{y^{4}}}{{y^{8}z^{-2}}} = \dfrac{{y^{4}}}{{y^{8}}} \cdot \dfrac{{1}}{{z^{-2}}} = y^{{4} - {8}} \cdot z^{- {(-2)}} = y^{-4}z^{2} |
-19,738 | \frac{35}{8} = 5 \cdot 7/(8) |
178 | x = x \times 0 \Rightarrow x = 0 |
-1,495 | -\dfrac75\cdot 5/2 = \frac{\frac{1}{2}\cdot 5}{\left(-5\right)\cdot 1/7} |
9,566 | \frac{2*y}{\sqrt{1 + y^2} + y + (-1)} = \dfrac{1}{y + (-1) + \sqrt{1 + y^2}}*(y * y + 1 - y^2 + y*2 + (-1)) |
7,056 | \sin(\arccos(z)) = (1 - z^2)^{1/2} |
25,122 | 8!/(2!*3!) = 3360 |
20,087 | \binom{4}{2}*2*9! - 24*8! = 8!*84 |
22,914 | N \cdot A = N \cdot A |
-2,005 | \pi/2 = \pi/12 + \pi \cdot 5/12 |
21,764 | 2*(1 + n*2) = n*4 + 2 |
12,237 | 2*\pi + 0 = 2*\pi |
15,648 | \left(\tfrac{1}{e^0} + 0\right)*2 + 0 + 0 = 2 |
11,732 | x * x * x + \left(-1\right) = ((-1) + x)*(1 + x^2 + x) |
18,025 | 1 = det\left(A\cdot F\right) = det\left(A\right)\cdot det\left(F\right) |
16,869 | h \cdot m = h_1 \cdot m_1 \Rightarrow h_1 = m/(m_1) \cdot h |
4,149 | (n + 1) \cdot (2 + n) = 2 + n^2 + n \cdot 3 |
10,404 | (\frac{1}{2}(1 + 5^{1/2}))^2 = \left(5^{1/2} + 3\right)/2 |
23,554 | 8 = 2 + 3*2 |
-12,128 | \frac{1}{36}31 = \dfrac{1}{18 \pi}s*18 \pi = s |
15,532 | b = \arcsin{a}\Longrightarrow \sin{b} = a |
-26,401 | \gamma^l \gamma^n = \gamma^{l + n} |
20,666 | \frac{\mathrm{d}}{\mathrm{d}z} 1/z = -\dfrac{1}{z \cdot z} = -\frac{1}{z \cdot z} |
23,692 | \left(1 + x^k\right) \cdot (x^k + \left(-1\right)) = x^{k \cdot 2} + (-1) |
4,827 | (-1) + \int\limits_0^1 \frac{1}{x^2}\,dx = \lim_{x \to 0^+} \frac1x - 1 + (-1) |
28,787 | \dfrac{1}{2^{1/2}} \cdot 2^{(j + 1)/2} = 2^{j/2} |
-13,232 | \frac{0.000243}{-0.0009} = -0.27 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.