Here, we show you a step-by-step solved example of intégrales de fonctions polynomiales. This solution was automatically generated by our smart calculator:
Expand the integral $\int\left(x^2+2x+1\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
Apply the formula: $\int x^ndx$$=\frac{x^{\left(n+1\right)}}{n+1}+C$, where $n=2$
The integral $\int x^2dx$ results in: $\frac{x^{3}}{3}$
Apply the formula: $\int cxdx$$=c\int xdx$, where $c=2$
Apply the formula: $\int xdx$$=\frac{1}{2}x^2+C$
Apply the formula: $\frac{a}{b}c$$=\frac{ca}{b}$, where $a=1$, $b=2$, $c=2$, $a/b=\frac{1}{2}$ and $ca/b=2\cdot \left(\frac{1}{2}\right)x^2$
The integral $\int2xdx$ results in: $x^2$
Apply the formula: $\int cdx$$=cvar+C$, where $c=1$
The integral $\int1dx$ results in: $x$
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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