3.1895 \(\int (4 x+\pi x^3) \, dx\)

Optimal. Leaf size=14 \[ \frac{\pi x^4}{4}+2 x^2 \]

[Out]

2*x^2 + (Pi*x^4)/4

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Rubi [A]  time = 0.002349, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{\pi x^4}{4}+2 x^2 \]

Antiderivative was successfully verified.

[In]

Int[4*x + Pi*x^3,x]

[Out]

2*x^2 + (Pi*x^4)/4

Rubi steps

\begin{align*} \int \left (4 x+\pi x^3\right ) \, dx &=2 x^2+\frac{\pi x^4}{4}\\ \end{align*}

Mathematica [A]  time = 0.0000272, size = 14, normalized size = 1. \[ \frac{\pi x^4}{4}+2 x^2 \]

Antiderivative was successfully verified.

[In]

Integrate[4*x + Pi*x^3,x]

[Out]

2*x^2 + (Pi*x^4)/4

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Maple [A]  time = 0., size = 13, normalized size = 0.9 \begin{align*} 2\,{x}^{2}+{\frac{\pi \,{x}^{4}}{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Pi*x^3+4*x,x)

[Out]

2*x^2+1/4*Pi*x^4

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Maxima [A]  time = 0.985601, size = 16, normalized size = 1.14 \begin{align*} \frac{1}{4} \, \pi x^{4} + 2 \, x^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(pi*x^3+4*x,x, algorithm="maxima")

[Out]

1/4*pi*x^4 + 2*x^2

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Fricas [A]  time = 2.01498, size = 27, normalized size = 1.93 \begin{align*} \frac{1}{4} \, \pi x^{4} + 2 \, x^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(pi*x^3+4*x,x, algorithm="fricas")

[Out]

1/4*pi*x^4 + 2*x^2

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Sympy [A]  time = 0.052748, size = 10, normalized size = 0.71 \begin{align*} \frac{\pi x^{4}}{4} + 2 x^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(pi*x**3+4*x,x)

[Out]

pi*x**4/4 + 2*x**2

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Giac [A]  time = 1.05804, size = 16, normalized size = 1.14 \begin{align*} \frac{1}{4} \, \pi x^{4} + 2 \, x^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(pi*x^3+4*x,x, algorithm="giac")

[Out]

1/4*pi*x^4 + 2*x^2