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