Common Monomial Factor Calculator

The integral of the inverse of the lineal function is given by the following formula, $\displaystyle\int\frac{1}{x}dx=\ln(x)$

Expand the fraction $\frac{1-x}{x^2}$ into $2$ simpler fractions with common denominator $x^2$

Simplify the resulting fractions

Expand the integral $\int\left(\frac{1}{x^2}+\frac{-1}{x}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

The integral of the inverse of the lineal function is given by the following formula, $\displaystyle\int\frac{1}{x}dx=\ln(x)$

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $-2$

Simplify the expression inside the integral

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

Take the variable outside of the logarithm

Simplifying the logarithm

Simplify $e^{\left(\frac{1}{-x}-\ln\left(x\right)+C_0\right)}$ by applying the properties of exponents and logarithms

Simplify $e^{\left(\frac{1}{-x}+C_0\right)}$ applying properties of exponents

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

Any expression to the power of $1$ is equal to that same expression

Multiply the fraction and term