Integrate int(x(3x^2)^(1/2)+1)dx

 Exercise

$\int x\sqrt{3x^2}+1dx$

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Expand the integral $\int\left(x\sqrt{3x^2}+1\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int x\sqrt{3x^2}dx+\int1dx$

 

The integral $\int x\sqrt{3x^2}dx$ results in: $\frac{\sqrt{3}x^{3}}{3}$

$\frac{\sqrt{3}x^{3}}{3}$

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The integral $\int1dx$ results in: $x$

$x$

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Gather the results of all integrals

$\frac{\sqrt{3}x^{3}}{3}+x$

 

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

$\frac{\sqrt{3}x^{3}}{3}+x+C_0$

$\frac{\sqrt{3}x^{3}}{3}+x+C_0$

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