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

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

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {\pi x^4}{4}+2 x^2 \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {\pi x^4}{4}+2 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[4*x + Pi*x^3,x]

[Out]

2*x^2 + (Pi*x^4)/4

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (4 x+\pi x^3\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[4*x + Pi*x^3,x]

[Out]

IntegrateAlgebraic[4*x + Pi*x^3, x]

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fricas [A]  time = 0.71, size = 12, normalized size = 0.86 \begin {gather*} \frac {1}{4} \, \pi x^{4} + 2 \, x^{2} \end {gather*}

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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giac [A]  time = 1.06, size = 12, normalized size = 0.86 \begin {gather*} \frac {1}{4} \, \pi x^{4} + 2 \, x^{2} \end {gather*}

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

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maple [A]  time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} \frac {1}{4} \pi \,x^{4}+2 x^{2} \end {gather*}

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 = 1.00, size = 12, normalized size = 0.86 \begin {gather*} \frac {1}{4} \, \pi x^{4} + 2 \, x^{2} \end {gather*}

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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mupad [B]  time = 0.02, size = 12, normalized size = 0.86 \begin {gather*} \frac {\Pi \,x^4}{4}+2\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x + Pi*x^3,x)

[Out]

(Pi*x^4)/4 + 2*x^2

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sympy [A]  time = 0.06, size = 10, normalized size = 0.71 \begin {gather*} \frac {\pi x^{4}}{4} + 2 x^{2} \end {gather*}

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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