Question

найдите первообразную функции f(x) = sinx* cos4x

Answer 1

$f(x)=\sin x\cos4x=\frac12\left(\sin(x-4x)+\sin(4+x)\right)=\frac12(\sin(-3x)+\sin5x)=\\=\frac12(\sin5x-\sin3x)\\F(x)=\frac12(-\frac15\cos5x+\frac13\cos3x)=\frac16\cos3x-\frac1{10}\cos5x+C$