Separable Differential Equations Calculator

Multiply the fraction by the term

Any expression multiplied by $1$ is equal to itself

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

Divide $x^2-4$ by $x+4$

Resulting polynomial

Expand the integral $\int\left(x-4+\frac{12}{x+4}\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately

We can solve the integral $\int\frac{12}{x+4}dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $x+4$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

Now, in order to rewrite $dx$ in terms of $du$, we need to find the derivative of $u$. We need to calculate $du$, we can do that by finding the derivative of the equation above

Substituting $u$ and $dx$ in the integral and simplify

The integral of a constant is equal to the constant times the integral's variable

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

Replace $u$ with the value that we assigned to it in the beginning: $x+4$

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, in this case $n=1$

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