What is the integral of (sin(y))/x ?

The integral of (sin(y))/x is sin(y)ln|x|+C

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integral of (sin(y))/x

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

sin (y) ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= sin (y) \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= sin (y) ln ∣ x ∣

Add a constant to the solution

= sin (y) ln ∣ x ∣ + C

f (x) = \frac{r}{r ^{2} + 5}

\frac{d}{d x} (g (x) (x^{3}))

\frac{\partial}{\partial x} (y x^{2} + 6 x^{3} + x y)

\frac{\partial}{\partial x} (x^{2} + y^{2} + x^{2} y + 4)

What is the integral of (sin(y))/x ?
The integral of (sin(y))/x is sin(y)ln|x|+C