import sympy as sp
from IPython.display import display

a,x = sp.symbols('a x',real=True)
eq=[x*sp.sqrt(x**2+1),sp.cos(x)**2*sp.sin(x)]
for f in eq:  
    display(sp.Eq(sp.Integral(f, x), 
                  sp.simplify(sp.Integral(f, x).doit())))