3.19.95 \(\int (4 x+\pi x^3) \, dx\) [1895]

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

[Out]

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

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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*} 2 x^2+\frac {\pi x^4}{4} \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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Maple [A]
time = 0.04, size = 15, normalized size = 1.07

method	result	size
gosper	\(\frac {x^{2} \left (\pi \,x^{2}+8\right )}{4}\)	\(13\)
norman	\(2 x^{2}+\frac {1}{4} \pi \,x^{4}\)	\(13\)
risch	\(2 x^{2}+\frac {1}{4} \pi \,x^{4}\)	\(13\)
default	\(\frac {\left (\pi \,x^{2}+4\right )^{2}}{4 \pi }\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Pi*x^3+4*x,x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.27, 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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Fricas [A]
time = 0.56, 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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Sympy [A]
time = 0.01, 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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Giac [A]
time = 1.55, 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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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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