Optimal. Leaf size=19 \[ -\frac {2}{7 b x^2 \sqrt {b x^3}} \]
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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 {2}{7 b x^2 \sqrt {b x^3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (b x^3\right )^{3/2}} \, dx &=\frac {x^{3/2} \int \frac {1}{x^{9/2}} \, dx}{b \sqrt {b x^3}}\\ &=-\frac {2}{7 b x^2 \sqrt {b x^3}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.74 \begin {gather*} -\frac {2 x}{7 \left (b x^3\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 11, normalized size = 0.58
method | result | size |
gosper | \(-\frac {2 x}{7 \left (b \,x^{3}\right )^{\frac {3}{2}}}\) | \(11\) |
default | \(-\frac {2 x}{7 \left (b \,x^{3}\right )^{\frac {3}{2}}}\) | \(11\) |
trager | \(-\frac {2 \sqrt {b \,x^{3}}}{7 b^{2} x^{5}}\) | \(16\) |
risch | \(-\frac {2}{7 b \,x^{2} \sqrt {b \,x^{3}}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 10, normalized size = 0.53 \begin {gather*} -\frac {2 \, x}{7 \, \left (b x^{3}\right )^{\frac {3}{2}}} \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 {2 \, \sqrt {b x^{3}}}{7 \, 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 = 14, normalized size = 0.74 \begin {gather*} - \frac {2 x}{7 \left (b x^{3}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.72, size = 17, normalized size = 0.89 \begin {gather*} -\frac {2}{7 \, \sqrt {b x} b x^{3} \mathrm {sgn}\left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.94, size = 15, normalized size = 0.79 \begin {gather*} -\frac {2\,\sqrt {b\,x^3}}{7\,b^2\,x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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