Optimal. Leaf size=13 \[ x^2+\frac {x^3}{3}+\log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \frac {x^3}{3}+x^2+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (\frac {1}{x}+2 x+x^2\right ) \, dx &=x^2+\frac {x^3}{3}+\log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} x^2+\frac {x^3}{3}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 0.92
method | result | size |
default | \(x^{2}+\frac {x^{3}}{3}+\ln \left (x \right )\) | \(12\) |
norman | \(x^{2}+\frac {x^{3}}{3}+\ln \left (x \right )\) | \(12\) |
risch | \(x^{2}+\frac {x^{3}}{3}+\ln \left (x \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 11, normalized size = 0.85 \begin {gather*} \frac {1}{3} \, x^{3} + x^{2} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.74, size = 11, normalized size = 0.85 \begin {gather*} \frac {1}{3} \, x^{3} + x^{2} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 10, normalized size = 0.77 \begin {gather*} \frac {x^{3}}{3} + x^{2} + \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.84, size = 12, normalized size = 0.92 \begin {gather*} \frac {1}{3} \, x^{3} + x^{2} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 11, normalized size = 0.85 \begin {gather*} \ln \left (x\right )+x^2+\frac {x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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