Optimal. Leaf size=19 \[ \frac {x^5}{4 b \sqrt {b x^2}} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 30}
\begin {gather*} \frac {x^5}{4 b \sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {x^6}{\left (b x^2\right )^{3/2}} \, dx &=\frac {x \int x^3 \, dx}{b \sqrt {b x^2}}\\ &=\frac {x^5}{4 b \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 0.84 \begin {gather*} \frac {x^7}{4 \left (b x^2\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 13, normalized size = 0.68
method | result | size |
gosper | \(\frac {x^{7}}{4 \left (b \,x^{2}\right )^{\frac {3}{2}}}\) | \(13\) |
default | \(\frac {x^{7}}{4 \left (b \,x^{2}\right )^{\frac {3}{2}}}\) | \(13\) |
risch | \(\frac {x^{5}}{4 b \sqrt {b \,x^{2}}}\) | \(16\) |
trager | \(\frac {\left (x^{3}+x^{2}+x +1\right ) \left (x -1\right ) \sqrt {b \,x^{2}}}{4 b^{2} x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 15, normalized size = 0.79 \begin {gather*} \frac {x^{5}}{4 \, \sqrt {b x^{2}} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 15, normalized size = 0.79 \begin {gather*} \frac {\sqrt {b x^{2}} x^{3}}{4 \, b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.26, size = 12, normalized size = 0.63 \begin {gather*} \frac {x^{7}}{4 \left (b x^{2}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.23, size = 12, normalized size = 0.63 \begin {gather*} \frac {x^{4}}{4 \, b^{\frac {3}{2}} \mathrm {sgn}\left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {x^6}{{\left (b\,x^2\right )}^{3/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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