Solve ∫ sin(y)/y wrt x

$$\int{ \frac{ \sin ( y ) }{ y } }d x$$

Evaluate

$$\frac{x\sin(y)}{y}+С$$

Solution Steps

Find the integral of \frac{\sin(y)}{y} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{\sin(y)}{y}x$$

Simplify.

$$\frac{\sin(y)x}{y}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{\sin(y)x}{y}+С$$

Differentiate w.r.t. x

$$\frac{\sin(y)}{y}$$