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ddrg
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math_formulas

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-27,515
2 \cdot a \cdot a \cdot 3 \cdot 2 = a^2 \cdot 12
5,624
dx' = x' d
-5,618
\frac{1}{2\cdot (x + 8\cdot \left(-1\right))}\cdot 2 = \dfrac{1}{x\cdot 2 + 16\cdot (-1)}\cdot 2
-18,391
\tfrac{1}{i^2 + 7i}(42 + i^2 + 13 i) = \frac{1}{i*(i + 7)}\left(7 + i\right) \left(i + 6\right)
31,739
-\left((-m*2)^{1/2}\right)^2 = 2*m
169
E \cdot \Sigma \cdot T = \Sigma \cdot E \cdot T
-20,118
\dfrac99 \frac{8 (-1) + x*2}{x + 10 \left(-1\right)} = \dfrac{72 \left(-1\right) + x*18}{x*9 + 90 \left(-1\right)}
929
x^2 + b\cdot x rightarrow -\left(\frac{b}{2}\right)^2 + \left(\frac{b}{2} + x\right) \cdot \left(\frac{b}{2} + x\right)
11,300
e^C*e^W = e^{W + C}
3,927
x A = x x A \implies x \in A
28,300
(3 + w)^2 + 14 = w^2 + w \times 6 + 23
11,055
(y^{2g_1})^{g_2} = \left((y^{g_1})^2\right)^{g_2} = (\frac{1}{y^{g_1}})^{g_2} = (y^{g_1})^{g_2 + (-1)}
11,938
4*k + 4 = 4*\left(k + 1\right)
45,503
11\times 59 = 649
-23,108
-\dfrac74 = \dfrac72\cdot (-\frac{1}{2})
17,147
6 + x^2 - 5\cdot x = (x + 2\cdot (-1))\cdot (x + 3\cdot (-1))
2,445
\Delta_1 \cdot \Delta_2 \cdot \Delta_1 \cdot \Delta_2 = \Delta_2 \cdot \Delta_1 \cdot \Delta_2 \cdot \Delta_1
24,763
-\sin{a} \cdot \sin{b} + \cos{b} \cdot \cos{a} = \cos(a + b)
34,297
\sec^2\left(x\right) + (-1) = \tan^2\left(x\right)
44,965
1+6+15 = 22
5,319
10 = ((-1) + 6)*2
21,852
\alpha\cdot |Z|^2 + \beta\cdot |Z \cdot Z| = \alpha\cdot |Z|^2 + \beta\cdot |Z|^2 = \left(\alpha + \beta\right)\cdot |Z|^2
-22,204
k^2 - 3k + 2 = (\left(-1\right) + k) (2(-1) + k)
20,019
\cos{x} = \frac{1}{\sqrt{1 + \tan^2{x}}} \lt \frac{1}{\sqrt{1 + x^2}}
-27,563
\frac{dy}{dx} = \dfrac{(-1)\cdot (6\cdot x \cdot x - 5\cdot y)}{(-1)\cdot (5\cdot x + 2\cdot y)} = \frac{6\cdot x^2 - 5\cdot y}{5\cdot x + 2\cdot y}
-10,456
2/2 \cdot (-\frac{1}{5 \cdot q^2} \cdot (q + 7 \cdot (-1))) = -\frac{1}{q \cdot q \cdot 10} \cdot (2 \cdot q + 14 \cdot (-1))
-3,699
\tfrac{1}{20}*18*\frac{i^5}{i} = \tfrac{18*i^5}{20*i}
35,450
\int |c|\,d\nu = \int |c|\,d\nu
11,564
\cosh(2 \cdot t) = \cosh^2(t) + \sinh^2(t) = 1 + 2 \cdot \sinh^2(t)
34,862
\nu^3 = y^3 = z^2 * z = \nu*y*z
34,776
(2n-3)!! = \frac{(2n-2)!!}{(2n-2)!!}(2n-3)!! = \frac{(2n-2)!}{(2n-2)!!} = \frac{(2n-2)!}{2^{n-1}(n-1)!}
10,397
2\theta = \frac13\left(2n + 1\right) \pi\Longrightarrow \pi\cdot (n\cdot 2 + 1)/6 = \theta
-2,429
12 \cdot 6^{1 / 2} = (3 + 4 + 5) \cdot 6^{1 / 2}
37,367
\cos{2\cdot \xi} = \cos^2{\xi} - \sin^2{\xi} = 2\cdot \cos^2{\xi} + \left(-1\right)
-613
11/2 \pi - 4\pi = 3/2 \pi
25,649
z\cdot (-1 + 1) = z - z
3,648
1 + z + za + z^2 + az^2 + a^2 z^2 + \dots = 1 + (1 + a) z + z^2*(a^2 + 1 + a) + \dots
12,851
\tfrac{1}{(4^4)^2}4!^2 = 9/1024 \approx 0.008789
-11,748
\left(9/4\right)^2 = \frac{1}{16} \cdot 81
21,174
(x + 2\times Z + 3\times z)^2 = Z\times x\times 4 + x^2 + 4\times Z \times Z + 9\times z^2 + 12\times Z\times z + x\times z\times 6
3,500
\frac 12=\frac 1k\Rightarrow k=2
-4,360
\dfrac{66 \cdot t}{48 \cdot t^4} = \frac{t}{t^4} \cdot 66/48
11,955
\frac12\cdot (a + f) = -\dfrac12\cdot (f - a) + f
11,453
(y + 1) \cdot \left(y \cdot y - y + 2\right) = (y + 1) \cdot (y^2 - y + 1) + y + 1 = y \cdot y^2 + 1 + y + 1 = 6 + y
15,668
1/4 \cdot \frac{1/4}{4} \cdot 1/4 \cdot 4/4 = \dfrac{4}{4^5}
-7,570
\tfrac{1}{18}(36 - 36 i - 36 i + 36 (-1)) = \frac{1}{18}(0 - 72 i) = -4i
42,464
e^{i\times j} = \cos{j} + i\times \sin{j} = \cosh{i} + j\times \sinh{i}
13,829
-t^2 + a \times t = a^2/4 - (t - a/2)^2
26,625
\dfrac12 \cdot \sin\left(x \cdot 2\right) = \cos(x) \cdot \sin\left(x\right)
14,779
16 (-1) + y^8 = (4 + y^4) (2 + y^2) (y^2 + 2 (-1))
-594
e^{\frac{23}{12} \cdot i \cdot \pi \cdot 15} = (e^{23 \cdot \pi \cdot i/12})^{15}
12,432
f = i v + u\Longrightarrow -v + i u = i f
15,215
\cot(x + 2 \cdot \pi) = \cot\left(x\right)
658
\frac{c^n - k^n}{c - k} = c^{n + (-1)} + ... + c^2 k^{3(-1) + n} + k^{n + 2(-1)} c + k^{n + (-1)}
16,481
25 + x^2 + x \cdot 2 = \left(x + 1\right)^2 + 24
-19,729
\frac{21}{8}\cdot 1 = 21/8
-10,663
\frac{1}{b^2} \cdot 2 \cdot 12/12 = \frac{24}{12 \cdot b^2}
17,453
\dfrac{1}{(3 + 1)^{1/2}\cdot 2} = 1/4
-7,541
\frac{1}{3 + 5 \cdot i} \cdot (-5 \cdot i - 37) \cdot \dfrac{3 - 5 \cdot i}{3 - 5 \cdot i} = \frac{-37 - 5 \cdot i}{i \cdot 5 + 3}
30,676
(1 + k)^3 - k \cdot k \cdot k = 3\cdot k^2 + k\cdot 3 + 1
29,071
(x^2 + (-1))*(x^4 + x^2 + 1) = x^6 + (-1)
209
\frac{\text{d}}{\text{d}x} (5 + x)^5 = (5 + x)^4 \cdot 5
4,787
|4 + 2 \left(-1\right)| = |1 + 3 (-1)|
-1,744
3/4\cdot \pi + \pi = \frac14\cdot 7\cdot \pi
27,922
|f\cdot x| = |f|\cdot |x|
-27,628
13 + 13\cdot (-1) + 9\cdot \left(-1\right) + 2 = 0 + 9\cdot (-1) + 2 = -9 + 2 = -7
24,502
-x^2 + m^2 = \left(x + m\right) \cdot (m - x)
1,334
{x + m + (-1) \choose 2\cdot m + \left(-1\right)} = {x + m + (-1) \choose x + m + (-1) - 2\cdot m + (-1)} = {x + m + (-1) \choose x - m}
8,889
\sin\left(x\right) = \sin(y) = -\sin\left(x + y\right)
-10,364
\frac{1}{10 \cdot y} \cdot 4 \cdot \frac{1}{2} \cdot 2 = \frac{1}{y \cdot 20} \cdot 8
2,621
(5 \cdot \left(-1\right) + 10) \cdot (2^2 \cdot 5 + 2 \cdot 5 + 5) \cdot (10 + 5 \cdot (-1)) = -5 \cdot 5 \cdot 5 + 10^3
-6,625
\frac{5}{3*(p + 8)} = \frac{5}{3*p + 24}
10,632
(3^y + (-1))/2 = 1 + 3 + 3^2 + \dots + 3^{y + (-1)}
12,077
4*(-1) + 13 + 3*(-1) = 6
-19,013
\tfrac12 = \dfrac{A_s}{16*\pi}*16*\pi = A_s
25,990
(10^x + \left(-1\right)) (10^x + \left(-1\right)) = 10^{2 x} - 2*10^x + 1 \lt 10^{2 x}
-15,924
-\frac{44}{10} = \frac{10}{10} - 6\cdot \frac{9}{10}
172
(2*(-1) + x)*(x + 1) = x^2 - x + 2*(-1)
20,146
\cos 2A = 2 \cos^2 A - 1 = 1 - 2\sin^2 A
27,089
f\cdot d + d\cdot h = d\cdot (f + h)
12,623
\left(-1\right)\cdot (-1)\cdot (-1)\cdot 2 = -2
-7,930
(72 + 8 \cdot i - 90 \cdot i + 10)/41 = (82 - 82 \cdot i)/41 = 2 - 2 \cdot i
5,724
9 \cdot t \cdot t = x^2 \cdot 3 \Rightarrow 3 \cdot t^2 = x^2
-4,629
\frac{-x \cdot 2 + 7}{x^2 - 7 \cdot x + 12} = -\frac{1}{x + 4 \cdot \left(-1\right)} - \dfrac{1}{x + 3 \cdot (-1)}
-20,058
\dfrac{1}{k + 9}(6(-1) - k \cdot 6) \cdot 9/9 = \frac{54 (-1) - 54 k}{81 + k \cdot 9}
-23,082
-\frac32 \cdot (-2) = 3
32,102
\frac{8}{2 \cdot h^2} \cdot h \cdot h \cdot h = 4 \cdot h
17,477
2x + 8\left(-1\right) = (x + 4\left(-1\right))*2
11,837
\cos\left(E\right) \cdot \sin(Z) + \sin(E) \cdot \cos(Z) = \sin(Z + E)
20,735
a^3-b^3 = (a-b)(a^2 + ab + b^2)
20,651
\left\lfloor{z^2}\right\rfloor + (-1) = \left\lfloor{z^2 + (-1)}\right\rfloor
-7,447
1/12 = 3/8*\frac{1}{9}*4*\frac{5}{10}
-23,448
3/5 \cdot 5/9 = \dfrac{1}{3}
12,853
3^6*2^6*4^3 = 2^1*3^2*4^3*2^5*3^4
10,606
(10+10)\times0=0
-24,669
8 + i \cdot 52 = 9 + i \cdot 52 + (-1)
46,354
\cos{N} = \cos{-N}
19,096
\cos(2 \cdot t) = 1 - 2 \cdot \sin^2(t) = 2 \cdot \cos^2\left(t\right) + (-1)
-29,144
4 \cdot 4 + 1\cdot 2 = 18
-12,113
14/15 = \tfrac{1}{6 \cdot \pi} \cdot t \cdot 6 \cdot \pi = t