Первообразная [latex] \frac{1}{sin^25x} [/latex] равна [latex]-ctg5x?[/latex]

[latex]\int\frac{1}{sin^2(5x)}dx=[d(5x)=5dx\rightarrow dx=\frac{d(5x)}{5}]=\int\frac{1}{sin^2(5x)}*\frac{d(5x)}{5}=\\=\frac{1}{5}\int\frac{d(5x)}{sin^2(5x)}=\frac{1}{5}*(-ctg(5x))=-\frac{ctg(5x)}{5}[/latex]