import sympy as sp
from IPython.display import display

x = sp.symbols('x',real=True)
for n in range(10,14):
    eq = (sp.sin(x))**n
    display(sp.Eq(sp.Integral(eq,(x,0,sp.pi/2)),
                  sp.simplify(sp.integrate(eq,(x,0,sp.pi/2)))))