Question

Найдите F(x)
f(x)=sin^2*3x

Answer 1

$f(x)=sin^23x\\\\F(x)=\int f(x)\, dx=\int sin^23x\, dx=\int \frac{1-cos6x}{2}\, dx=\frac{1}{2}\int (1-cos6x)\, dx=\\\\=\frac{1}{2}\cdot (x-\frac{1}{6}\, cos6x)+C=\frac{x}{2}-\frac{1}{12}\, cos6x+C$