What is the integral of (y-2)/x ?

The integral of (y-2)/x is 1/x (-2y+(y^2)/2)+C

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integral of (y-2)/x

integral

\frac{y - 2}{x}

\frac{1}{x} (- 2 y + \frac{y ^{2}}{2}) + C

Solution steps

\int \frac{y - 2}{x} d y

Take the constant out:

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

= \frac{1}{x} \cdot \int - 2 + y d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{x} (- \int 2 d y + \int y d y)

\int 2 d y = 2 y

\int y d y = \frac{y ^{2}}{2}

= \frac{1}{x} (- 2 y + \frac{y ^{2}}{2})

Add a constant to the solution

= \frac{1}{x} (- 2 y + \frac{y ^{2}}{2}) + C

in t e g r a l \frac{x ( 1 + 3 x ^{2} ) ^{5}}{2}

in t e g r a l \frac{2}{t ^{3}}

in t e g r a l \frac{x}{sin ^{2} ( x ^{2} )}

in t e g r a l \frac{x}{16}

in t e g r a l \frac{cos ^{2} ( 2 x )}{sin ( 2 x )}

What is the integral of (y-2)/x ?
The integral of (y-2)/x is 1/x (-2y+(y^2)/2)+C