Optimal. Leaf size=19 \[ \frac {1}{6} b^2 x^5 \sqrt {b x^2} \]
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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 = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30}
\begin {gather*} \frac {1}{6} b^2 x^5 \sqrt {b x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (b x^2\right )^{5/2} \, dx &=\frac {\left (b^2 \sqrt {b x^2}\right ) \int x^5 \, dx}{x}\\ &=\frac {1}{6} b^2 x^5 \sqrt {b x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{6} x \left (b x^2\right )^{5/2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 11, normalized size = 0.58
method | result | size |
gosper | \(\frac {x \left (b \,x^{2}\right )^{\frac {5}{2}}}{6}\) | \(11\) |
default | \(\frac {x \left (b \,x^{2}\right )^{\frac {5}{2}}}{6}\) | \(11\) |
risch | \(\frac {b^{2} x^{5} \sqrt {b \,x^{2}}}{6}\) | \(16\) |
trager | \(\frac {b^{2} \left (x^{5}+x^{4}+x^{3}+x^{2}+x +1\right ) \left (x -1\right ) \sqrt {b \,x^{2}}}{6 x}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 10, normalized size = 0.53 \begin {gather*} \frac {1}{6} \, \left (b x^{2}\right )^{\frac {5}{2}} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{6} \, \sqrt {b x^{2}} b^{2} x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.21, size = 10, normalized size = 0.53 \begin {gather*} \frac {x \left (b x^{2}\right )^{\frac {5}{2}}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.53, size = 10, normalized size = 0.53 \begin {gather*} \frac {1}{6} \, b^{\frac {5}{2}} x^{6} \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 {\left (b\,x^2\right )}^{5/2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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