## Solution for $\mathbb{u}_v$

In this notebook we validate our solution to the integral $\mathbb{u}$.


```python
import sympy
from sympy import *
from sympy.assumptions import assuming, Q
from sympy.assumptions.assume import global_assumptions
```


```python
# Initialize the session
init_session(quiet=True)
print("Using sympy version", sympy.__version__)

# Define our symbols
phi = symbols('phi')
v = symbols('v', integer=True)
global_assumptions.add(Q.positive(v))
```

    
    Using sympy version 1.4



```python
integrate(
    cos(phi) * sin(phi) ** (2 * v + 1),
    phi
)
```

We only need this integral for $v \ge 0$, so the indefinite integral is

$
\frac{\sin^{2v + 2}\phi}{2v + 2}
$

as expected.

7ca3dc9048b7e5b6415edd0477e0e830149983c6
ipynb
Jupyter Notebook
tex/proofs/U.ipynb
rodluger/starrynight
d3f015e466621189cb271d4d18b538430b14a557
MIT
2020-05-20T09:30:30.000Z
2021-06-27T14:17:33.000Z
tex/proofs/U.ipynb
rodluger/starrynight
d3f015e466621189cb271d4d18b538430b14a557
MIT
2020-05-16T18:49:42.000Z
2021-02-11T21:46:32.000Z
tex/proofs/U.ipynb
rodluger/starrynight
d3f015e466621189cb271d4d18b538430b14a557
MIT
2020-05-19T17:11:57.000Z
2020-05-19T17:11:57.000Z
Qwen/Qwen-72B
1. YES
2. YES