Here, we show you a step-by-step solved example of integrals of rational functions. This solution was automatically generated by our smart calculator:
Divide $2x^5-10x^3-2x^2+10$ by $x^2-5$
Resulting polynomial
Expand the integral $\int\left(2x^{3}-2\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
The integral of a function times a constant ($2$) is equal to the constant times the integral of the function
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 $3$
Simplify the fraction $2\left(\frac{x^{4}}{4}\right)$
The integral $\int2x^{3}dx$ results in: $\frac{1}{2}x^{4}$
The integral of a constant is equal to the constant times the integral's variable
The integral $\int-2dx$ results in: $-2x$
Gather the results of all integrals
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
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