Lösung 2.1:5b

Aus Online Mathematik Brückenkurs 2

The integral is not in our list of known integrals, but we will try to rewrite the integrand as something more manageable.

In this case, we can use the formula for half-angles and write

The right-hand side contains only terms which we can integrate and the calculation becomes

sin2xdx=21−cos2xdx=21−21cos2xdx=x2−212sin2x+C=x2−4sin2x+C.

(Notice how we compensate with a factor 2 in the denominator for the inner derivative of sin2x.)