```python
from sympy import *
```


```python
x, y, z, t = symbols('x y z t')
k, m, n = symbols('k m n', integer=True)
f, g, h = symbols('f g h', cls=Function)
```


```python
eq = Eq(x**2 - x + 2)
eq
```




$\displaystyle x^{2} - x + 2 = 0$




```python
solveset(eq, x)
```




$\displaystyle \left\{\frac{1}{2} - \frac{\sqrt{7} i}{2}, \frac{1}{2} + \frac{\sqrt{7} i}{2}\right\}$




```python
inte = Integral(sin(x)**6 * cos(x) ** 2, (x, pi / 3,  pi / 2))
inte
```




$\displaystyle \int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$




```python
inte.doit()
```




$\displaystyle \frac{9 \sqrt{3}}{2048} + \frac{5 \pi}{768}$




```python
inte2 = Integral(exp(-4 * x)* cos(3 * x), (x, 0, pi / 4))
inte2
```




$\displaystyle \int\limits_{0}^{\frac{\pi}{4}} e^{- 4 x} \cos{\left(3 x \right)}\, dx$




```python
inte2.doit()
```




$\displaystyle \frac{7 \sqrt{2}}{50 e^{\pi}} + \frac{4}{25}$




```python
inte3 = Integral(1/ (x**2 * (x - 4)), (x, 1, 3))
inte3
```




$\displaystyle \int\limits_{1}^{3} \frac{1}{x^{2} \left(x - 4\right)}\, dx$




```python
inte3.doit()
```




$\displaystyle - \frac{1}{6} - \frac{\log{\left(3 \right)}}{8}$




```python
inte4 = Integral(sqrt(1-y**2), (y, 0, x))
inte4 = Integral(inte4, (x, 0, 1))
inte4
```




$\displaystyle \int\limits_{0}^{1}\int\limits_{0}^{x} \sqrt{1 - y^{2}}\, dy\, dx$




```python
inte4.doit()
```




$\displaystyle - \frac{1}{3} + \frac{\pi}{4}$




```python
inte5 = Integral(1 / (3*sin(x) + 4*cos(x)), (x, 0, pi / 2))
inte5
```




$\displaystyle \int\limits_{0}^{\frac{\pi}{2}} \frac{1}{3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}}\, dx$




```python
simplify(inte5.doit())
```




$\displaystyle \frac{\log{\left(6 \right)}}{5}$




```python
inte6 = Integral(1 / (sin(x) * cos(x) + cos(x)**2), (x, 0, pi / 4))
inte6
```




$\displaystyle \int\limits_{0}^{\frac{\pi}{4}} \frac{1}{\sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}}\, dx$




```python
inte6.doit()
```




$\displaystyle - \log{\left(\sqrt{2} \right)} + \log{\left(-1 - \left(-1 + \sqrt{2}\right)^{2} + 2 \sqrt{2} \right)} - \log{\left(2 - \sqrt{2} \right)}$




```python
simplify(inte6.doit())
```




$\displaystyle \log{\left(\frac{2 \sqrt{2} \left(-1 + \sqrt{2}\right)}{2 - \sqrt{2}} \right)}$




```python
# numerilical
nsimplify(inte6.doit())
```




$\displaystyle \log{\left(2 \right)}$




```python
sum1 = Sum(k**-2, (k, 1, oo))
sum1
```




$\displaystyle \sum_{k=1}^{\infty} \frac{1}{k^{2}}$




```python
sum1.doit()
```




$\displaystyle \frac{\pi^{2}}{6}$




```python

```

8f2f8b5d83f95e4b94b7bf5a5ffb931d5d5b768b
ipynb
Jupyter Notebook
hello-sympy.ipynb
mo-mo-666/hello-sympy
ec9783166ec42615f18b7c77a172b09687d8b143
MIT
hello-sympy.ipynb
mo-mo-666/hello-sympy
ec9783166ec42615f18b7c77a172b09687d8b143
MIT
2020-03-24T17:24:28.000Z
2020-03-31T03:14:26.000Z
hello-sympy.ipynb
mo-mo-666/hello-sympy
ec9783166ec42615f18b7c77a172b09687d8b143
MIT
Qwen/Qwen-72B
1. YES
2. YES