```python
from sympy import integrate, init_printing
from sympy.abc import x
init_printing(use_latex="mathjax")
```


```python
f = x**2 - 3*x + 2
integrate(f)

```




$\displaystyle \frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x$




```python
from sympy.abc import a,b,c
f = a*x**2+b*x+c
integrate(f, x)

```




$\displaystyle \frac{a x^{3}}{3} + \frac{b x^{2}}{2} + c x$




```python
from sympy import cos,pi

integrate(cos(x), (x,0,pi/2.0)) # from 0 to pi/2
```




$\displaystyle 1$




```python
integrate(x, (x,0,5))

```




$\displaystyle \frac{25}{2}$




```python
from sympy.abc import x,y,z,a,b,c,d
from sympy import simplify

```


```python
I1 = integrate(1, (y,c,d))
simplify( integrate(I1, (x,a,b) ) )

```




$\displaystyle \left(a - b\right) \left(c - d\right)$



[Referencia](https://numython.github.io/posts/integrales-con-sympy/)



```python
from __future__ import division
from sympy import *
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)

integrate(x**2 * exp(x) * cos(x), x)
```




$\displaystyle \frac{x^{2} e^{x} \sin{\left(x \right)}}{2} + \frac{x^{2} e^{x} \cos{\left(x \right)}}{2} - x e^{x} \sin{\left(x \right)} + \frac{e^{x} \sin{\left(x \right)}}{2} - \frac{e^{x} \cos{\left(x \right)}}{2}$




```python
integrate(5/(1+x**2), (x,-oo,oo))
```




$\displaystyle 5 \pi$



[Referencia](https://docs.sympy.org/latest/modules/integrals/integrals.html) [Comprobacion](https://www.youtube.com/watch?v=6uIeKpA2dHw) 


```python
f = sin(k*x)*cos(m*x)
integrate(f, x)
```




$\displaystyle \begin{cases} 0 & \text{for}\: k = 0 \wedge m = 0 \\\frac{\cos^{2}{\left(m x \right)}}{2 m} & \text{for}\: k = - m \\- \frac{\cos^{2}{\left(m x \right)}}{2 m} & \text{for}\: k = m \\- \frac{k \cos{\left(k x \right)} \cos{\left(m x \right)}}{k^{2} - m^{2}} - \frac{m \sin{\left(k x \right)} \sin{\left(m x \right)}}{k^{2} - m^{2}} & \text{otherwise} \end{cases}$




```python
f = sin(2*x)*cos(4*x)
integrate(f)
```




$\displaystyle \frac{\sin{\left(2 x \right)} \sin{\left(4 x \right)}}{3} + \frac{\cos{\left(2 x \right)} \cos{\left(4 x \right)}}{6}$




```python
limit(((x - 1)/(x + 1))**x, x, oo)
```




$\displaystyle e^{-2}$




```python
exp(-2)
```




$\displaystyle e^{-2}$




```python
limit(sin(x)/x, x, 2) 
```




$\displaystyle \frac{\sin{\left(2 \right)}}{2}$




```python
limit((1 - cos(x))/x**2, x, 0)
```




$\displaystyle \frac{1}{2}$




```python
 S.Half
    
```




$\displaystyle \frac{1}{2}$




```python
limit((1 + k/x)**x, x, oo) 

```




$\displaystyle e^{k}$




```python
 limit((x + 1)*(x + 2)*(x + 3)/x**3, x, oo) 
```




$\displaystyle 1$



[Referencia](https://github.com/sympy/sympy/blob/master/sympy/series/tests/test_demidovich.py)



```python
diff( cos(x) * (1 + x))
```




$\displaystyle - \left(x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)}$




```python
diff( cos(x) * (1 + x),x)
```




$\displaystyle - \left(x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)}$




```python
diff( cos(x) * (1 + x),x,x)
```




$\displaystyle - (\left(x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)})$




```python
diff(log(x * y), y) 
```




$\displaystyle \frac{1}{y}$



[Referencia](https://pybonacci.org/2012/04/30/como-calcular-limites-derivadas-series-e-integrales-en-python-con-sympy/)

02afebbaddcb7ecf3ebaf5fa6abfd8be4abcd33a
ipynb
Jupyter Notebook
LimitesDerivadasIntegrales/DerivadasLimitesIntegrales.ipynb
rulgamer03/Python-Projects
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2021-06-18T16:29:46.000Z
2021-06-18T16:29:46.000Z
LimitesDerivadasIntegrales/DerivadasLimitesIntegrales.ipynb
rulgamer03/Python-Projects
89a2418fadce0fd4674d3f7d3fa682a9aaa4b14d
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LimitesDerivadasIntegrales/DerivadasLimitesIntegrales.ipynb
rulgamer03/Python-Projects
89a2418fadce0fd4674d3f7d3fa682a9aaa4b14d
Apache-2.0
Qwen/Qwen-72B
1. YES
2. YES