var('x')
print("Elementary integrals:")

f = x^2
print(f.integrate(x))
print(integral(e^x,x))
print(integral(1/x,x))
print(integral(sinh(x), x))
print(integral(1/sqrt(1+x^2),x))

print("\nIntegration by parts:")
print(integral(e^x*cos(x), x))
print(integral(sqrt(x^2-25)/x, x))

print("\nDefinite integral:")
print(integral(1/(1+x^2), x, -1, 1))

print("\nImproper integral:")
print(integral(1/(1+x^2), x, -infinity, infinity))

print("\nDivergent integral:")
print(integral(1/(1-x), x, 1,2))    # Diverges