Optimal. Leaf size=23 \[ \frac {2 x^{5/2}}{5}+\frac {2 x^{3/2}}{15}-2 \log (x) \]
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Rubi [A] time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {2 x^{5/2}}{5}+\frac {2 x^{3/2}}{15}-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (-\frac {2}{x}+\frac {\sqrt {x}}{5}+x^{3/2}\right ) \, dx &=\frac {2 x^{3/2}}{15}+\frac {2 x^{5/2}}{5}-2 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \begin {gather*} \frac {2 x^{5/2}}{5}+\frac {2 x^{3/2}}{15}-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 26, normalized size = 1.13 \begin {gather*} \frac {2}{15} \left (3 x^{5/2}+x^{3/2}\right )-4 \log \left (\sqrt {x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.27, size = 19, normalized size = 0.83 \begin {gather*} \frac {2}{15} \, {\left (3 \, x^{2} + x\right )} \sqrt {x} - 4 \, \log \left (\sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.82, size = 16, normalized size = 0.70 \begin {gather*} \frac {2}{5} \, x^{\frac {5}{2}} + \frac {2}{15} \, x^{\frac {3}{2}} - 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.70 \begin {gather*} \frac {2 x^{\frac {5}{2}}}{5}+\frac {2 x^{\frac {3}{2}}}{15}-2 \ln \relax (x ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.03, size = 15, normalized size = 0.65 \begin {gather*} \frac {2}{5} \, x^{\frac {5}{2}} + \frac {2}{15} \, x^{\frac {3}{2}} - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.28, size = 17, normalized size = 0.74 \begin {gather*} \frac {2\,x^{3/2}}{15}-4\,\ln \left (\sqrt {x}\right )+\frac {2\,x^{5/2}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 20, normalized size = 0.87 \begin {gather*} \frac {2 x^{\frac {5}{2}}}{5} + \frac {2 x^{\frac {3}{2}}}{15} - 2 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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