# %%
# Python inizialisieren
import IPython.display as dp
import sympy as sp

sp.init_printing()

# Symbole
x = sp.symbols("x")
a = sp.symbols("a")
w = sp.symbols("w")

# Funktionen

funktionen = [
    x / (1 + x**4),
    (sp.exp(a * x)) * sp.sin(w * x),
    x**3 * sp.cos(x**2),
    x / sp.cos(x) ** 2,
    (sp.exp(2 * x)) / 1 + sp.exp(x),
    (sp.ln(x) ** 3) / x,
    sp.cos(sp.log(x)),
]

# Berechnung
for f in funktionen:
    F = sp.simplify(sp.integrate(f, x))
    dp.display(f)
    dp.display(F)
    print("---------------------------------------------")