Here, we show you a step-by-step solved example of intégrales de fonctions rationnelles. 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
Apply the formula: $\int cxdx$$=c\int xdx$, where $c=2$ and $x=x^{3}$
Apply the formula: $\int x^ndx$$=\frac{x^{\left(n+1\right)}}{n+1}+C$, where $n=3$
Apply the formula: $a\frac{x}{b}$$=\frac{a}{b}x$, where $a=2$, $b=4$, $ax/b=2\left(\frac{x^{4}}{4}\right)$, $x=x^{4}$ and $x/b=\frac{x^{4}}{4}$
The integral $\int2x^{3}dx$ results in: $\frac{1}{2}x^{4}$
Apply the formula: $\int cdx$$=cvar+C$, where $c=-2$
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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