Solve g=cos(3x)*dx

$$g = \cos ( 3 x ) \cdot d x$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{g}{x\cos(3x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{3}+\frac{\pi }{6}\text{ and }x\neq 0\\d\in \mathrm{C}\text{, }&\left(x=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{3}+\frac{\pi }{6}\right)\text{ and }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\cos(3x)dx=g$$

The equation is in standard form.

$$x\cos(3x)d=g$$

Divide both sides by \cos(3x)x.

$$\frac{x\cos(3x)d}{x\cos(3x)}=\frac{g}{x\cos(3x)}$$

Dividing by \cos(3x)x undoes the multiplication by \cos(3x)x.

$$d=\frac{g}{x\cos(3x)}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{g}{x\cos(3x)}\text{, }&x\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{3}+\frac{\pi }{6}\\d\in \mathrm{R}\text{, }&\left(\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{3}+\frac{\pi }{6}\text{ or }x=0\right)\text{ and }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\cos(3x)dx=g$$

The equation is in standard form.

$$x\cos(3x)d=g$$

Divide both sides by \cos(3x)x.

$$\frac{x\cos(3x)d}{x\cos(3x)}=\frac{g}{x\cos(3x)}$$

Dividing by \cos(3x)x undoes the multiplication by \cos(3x)x.

$$d=\frac{g}{x\cos(3x)}$$

Solve for g

$$g=dx\cos(3x)$$