What is the integral of (2z-5)/7 ?

The integral of (2z-5)/7 is 1/7 (z^2-5z)+C

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integral of (2z-5)/7

\int \frac{2 z - 5}{7} d z

\frac{1}{7} (z^{2} - 5 z) + C

Solution steps

\int \frac{2 z - 5}{7} d z

Take the constant out:

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

= \frac{1}{7} \cdot \int 2 z - 5 d z

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}{7} (\int 2 z d z - \int 5 d z)

\int 2 z d z = z^{2}

\int 5 d z = 5 z

= \frac{1}{7} (z^{2} - 5 z)

Add a constant to the solution

= \frac{1}{7} (z^{2} - 5 z) + C

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