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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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