import sympy as sp

t, tau = sp.symbols('t tau')
sol = sp.integrate(sp.sin(t - tau) * sp.cos(tau), (tau, 0, t))
print(sol)
# t*sin(t)/2

import numpy as np
from scipy import signal

t = np.linspace(-10, 10, 1000)
f = np.sin(t)
g = np.cos(t)
conv = 0.5 * t * np.sin(t)

print(conv)
# [-2.72  -2.63  -2.54  -2.449 -2.357 -2.264 -2.171 -2.078 -1.984 -1.89  ...,
#  -1.89  -1.984 -2.078 -2.171 -2.264 -2.357 -2.449 -2.54  -2.63  -2.72 ]

print(signal.convolve(f, g, mode='same'))
# [ 138.098  134.167  130.164  126.092  121.953  117.747  113.476  109.142
#   104.746  100.29  ...,  -95.775 -100.29  -104.746 -109.142 -113.476
#  -117.747 -121.953 -126.092 -130.164 -134.167]

n = 1000
t = np.linspace(0, 10, n)
dt = t[1] - t[0]
f = np.sin(t)
g = np.cos(t)
conv = 0.5 * t * np.sin(t)
conv2 = signal.convolve(f, g, mode='full')[:n] * dt
plt.plot(t, conv)   # assuming import matplotlib.pyplot as plt
plt.show()
plt.plot(t, conv2)
plt.show()