image imagewidth (px) 26 336 | latex stringlengths 2 482 | split stringclasses 4
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2 ^ { \frac { 1 } { 4 } } ( \frac { 5 + \sqrt { 5 } } { 5 - \sqrt { 5 } } ) ^ { \frac { 1 } { 4 } }
| 2016 | |
u _ { n } = 3 u _ { n - 2 } - u _ { n - 3 }
| train | |
4 ^ { 5 } - 4
| train | |
\int \limits _ { 0 } ^ { 1 } \int \limits _ { 0 } ^ { 1 } x ^ { 2 } y ^ { 2 } d x d y
| train | |
B . 1
| 2016 | |
C ( x - y )
| 2019 | |
\sum _ { n = 1 } ^ { N } ( - 1 ) ^ { n } \sin ( n x )
| train | |
8 \times 8 = 6 4
| train | |
[ x , y , z ] = ( x y ) z - x ( y z )
| 2019 | |
x ^ { y } - y ^ { x }
| train | |
\frac { 1 } { a } F ( a x + b ) + C
| train | |
( i , j , k )
| train | |
\sqrt { u } + H ^ { E }
| train | |
- | y | \leq y \leq | y |
| 2014 | |
( \gamma )
| train | |
5 9 - 1 3 5 + 1 2 5 \geq 4 8
| train | |
A = \sqrt { a + \frac { 1 } { \sqrt { a + \frac { 1 } { \sqrt { a } } } } } + \sqrt { b }
| train | |
3 0 \times 2 9 x ^ { 2 8 }
| train | |
y _ { n + 1 } = b x _ { n }
| train | |
y _ { m i n } = \frac { \alpha } { 2 m ^ { 2 } } + \sqrt { \frac { \alpha ^ { 2 } + 4 m ^ { 2 } \beta } { 4 m ^ { 2 } } }
| 2019 | |
1 + 1 6 + 1 2 0 + 1 0 = 1 4 7
| 2016 | |
x _ { a } x _ { a }
| 2016 | |
1 5 0 - ( ( 6 9 / 7 7 ) / 2 6 ) \neq - 1 0 7
| train | |
\sqrt { 1 + \sqrt { 2 + \sqrt { 3 + \sqrt { 4 } } } }
| train | |
\sin \theta = F _ { 0 6 }
| 2016 | |
( ( 9 5 - 8 6 ) \times 3 5 ) \times 1 9 7 \neq - 3 7 8 7 9
| train | |
2 ^ { n } - 1
| train | |
x ^ { 2 } + y ^ { 2 } = z ^ { 2 }
| train | |
\pi \int _ { c } ^ { d } \{ g ( y ) \} ^ { 2 } d y
| train | |
\int _ { n } ^ { \alpha } Y d k
| train | |
S \geq \sqrt { k }
| train | |
\frac { a } { \sin A } = \frac { b } { \sin B } = \frac { c } { \sin C }
| train | |
\frac { 2 4 3 } { 1 5 4 } = \frac { 3 } { 2 } + \frac { 6 } { 7 7 }
| 2016 | |
1 6 \times 2 \times 2 - ( 1 6 + 1 6 \times 2 ) = 1 6
| 2016 | |
[ \int u d c ]
| train | |
\sin x - \sin y - \sin ( x - y )
| train | |
\frac { x ^ { 4 } } { 2 ^ { 3 } } - ( \frac { 2 } { x } ) ^ { - 4 }
| train | |
\frac { ( n - 1 ) ( n + 2 ) } { n ( k + n ) } + \frac { 2 } { n k }
| 2016 | |
1 + 1 = 2
| train | |
z = \frac { - b } { a }
| 2019 | |
x ^ { y } - y ^ { x }
| train | |
\frac { x ^ { 2 } + y ^ { 2 } } { a ^ { 2 } } - \frac { z ^ { 2 } } { c ^ { 2 } } + 1 = 0
| train | |
u _ { n } = u _ { n - 1 } + u _ { n - 2 }
| train | |
\sqrt { s } , \sqrt { s - b } , \sqrt { s - a }
| 2019 | |
1 6 8 \pm ( 1 7 1 - 6 ) \div ( 2 4 \div 1 7 4 )
| train | |
A _ { 2 k } = \frac { 2 R A _ { k } } { 2 R + \sqrt { 4 R ^ { 2 } + A ^ { 2 } _ { k } } }
| train | |
\frac { 7 } { 2 }
| train | |
\int { d } ^ { 4 } x
| 2019 | |
y ^ { 4 } + y + 1 = 0
| train | |
g > 2 7
| train | |
f ( x ) = c \frac { 1 - e ^ { - x } } { 1 + e ^ { - x } }
| 2016 | |
\sqrt { r } + \sqrt { s } \geq 1
| 2019 | |
\frac { N + 9 } { \frac { B } { S } }
| train | |
\frac { 1 } { 3 } + \frac { 1 } { 3 }
| 2014 | |
1 + 1 = 2
| train | |
u ^ { 3 } + v ^ { 3 } = - \frac { 9 5 } { 5 4 }
| train | |
x = \sin ( y )
| train | |
y d x = a _ { 3 } d x x + b _ { 3 } d y x + c _ { 3 } d x y + d _ { 3 } d y y
| 2019 | |
\frac { 1 } { 2 } 4 \times 5 - 1 = 9
| 2019 | |
[ c ]
| train | |
r ( u , v )
| train | |
\int x \cos ( x ) d x = x \sin ( x ) - \int \sin ( x ) d x
| 2014 | |
\int \limits _ { a } ^ { b } f ( x ) d x = F ( b ) - F ( a )
| train | |
( ( 1 1 7 \times 5 4 ) \div ( 1 4 1 \times 1 2 4 ) ) - ( ( 7 0 \div 1 9 3 ) \div 1 5 9 ) \geq 0
| train | |
\cdots - \sum j
| train | |
d y ^ { 3 }
| train | |
B \times B
| 2016 | |
\lim _ { x \rightarrow - 1 } \frac { x ^ { 3 } + 1 } { x + 1 }
| train | |
3 ^ { n + 1 } + 2
| train | |
\sqrt { 1 + \sqrt { 2 + \sqrt { 3 + \sqrt { 4 } } } }
| train | |
\frac { - 1 + i \sqrt { 3 } } { 2 }
| train | |
x _ { x } ^ { x } + y _ { y } ^ { y } + z _ { z } ^ { z } - x - y - z
| train | |
2
| train | |
f ( x + r ) = f ( x )
| train | |
f ( x , y ) = f _ { 1 } ( x y ) + f _ { 2 } ( \frac { x } { y } )
| train | |
t = \frac { \pi } { 2 }
| train | |
\sqrt { \beta - Y _ { k } }
| train | |
8 9 \times ( 1 6 3 \times 4 0 ) \leq 5 8 0 2 8 0
| train | |
3 \times 3 + r - 3
| 2019 | |
\frac { x _ { 1 } } { \frac { x _ { 2 } } { \frac { x _ { 3 } } { x _ { 4 } } } }
| train | |
5 7
| train | |
f ( x , y ) = f _ { 1 } ( x , y ) + f _ { 2 } ( \frac { x } { y } )
| train | |
\frac { 5 } { x + 1 } + \frac { 5 } { x ^ { 2 } + x }
| train | |
j = 1 , 2
| train | |
\int F \neq 0
| 2016 | |
\int ( \sin ( t ) - t ) d t = - \cos ( t ) - \frac { 1 } { 2 } t ^ { 2 }
| 2014 | |
- 6 o
| train | |
\sin z < \beta
| 2016 | |
x ^ { 3 } - x ^ { 7 }
| 2019 | |
x - y
| 2016 | |
A _ { 2 k } = \frac { 2 R A _ { k } } { 2 R + \sqrt { 4 R ^ { 2 } + A ^ { 2 } _ { k } } }
| train | |
( a \frac { 1 - t ^ { 2 } } { 1 + t ^ { 2 } } , \frac { 2 b t } { 1 + t ^ { 2 } } )
| train | |
t _ { 1 } t _ { 2 } + t _ { 2 } t _ { 3 } + t _ { 3 } t _ { 1 }
| 2016 | |
\int d x _ { 5 } \int d x _ { 6 }
| 2016 | |
\int d z \int d w
| 2019 | |
5 0 ! \cdot n = 4 8 !
| train | |
z = \tan \alpha
| 2016 | |
3 ^ { 2 } - 1 = 8
| train | |
\sin \beta _ { n } x
| 2019 | |
x ^ { 2 } + y ^ { 2 } < 1
| train |
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