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