Final Answer
$\frac{1}{5}z-\frac{1}{5}\ln\left(z\right)+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{z-1}{5z}dz$
Specify the solving method
1
Expand the fraction $\frac{z-1}{5z}$ into $2$ simpler fractions with common denominator $5z$
$\int\left(\frac{z}{5z}+\frac{-1}{5z}\right)dz$
Learn how to solve integrals of rational functions problems step by step online.
$\int\left(\frac{z}{5z}+\frac{-1}{5z}\right)dz$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((z-1)/(5z))dz. Expand the fraction \frac{z-1}{5z} into 2 simpler fractions with common denominator 5z. Simplify the resulting fractions. Expand the integral \int\left(\frac{1}{5}+\frac{-1}{5z}\right)dz into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{5}dz results in: \frac{1}{5}z.
Final Answer
$\frac{1}{5}z-\frac{1}{5}\ln\left(z\right)+C_0$