Method $2$:

$sin(2x)=2sin(x)cos(x)$

Re$-$write the integrand and apply the double$-$angle formula

You may want to first adjust the double$-$angle formula by dividing by $2$

Use power$-$reducing formulas to re$-$write the integrand

When no powers of sine$/$cosine are greater than $1,$ you are ready to integrate

Substitution may be needed

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}si{n}^2(x)co{s}^2(x)dx$