Optimal. Leaf size=17 \[ -\frac {b \sqrt {b x^2}}{3 x^4} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, 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 {b \sqrt {b x^2}}{3 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\left (b x^2\right )^{3/2}}{x^7} \, dx &=\frac {\left (b \sqrt {b x^2}\right ) \int \frac {1}{x^4} \, dx}{x}\\ &=-\frac {b \sqrt {b x^2}}{3 x^4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 0.94 \begin {gather*} -\frac {\left (b x^2\right )^{3/2}}{3 x^6} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 13, normalized size = 0.76
method | result | size |
gosper | \(-\frac {\left (b \,x^{2}\right )^{\frac {3}{2}}}{3 x^{6}}\) | \(13\) |
default | \(-\frac {\left (b \,x^{2}\right )^{\frac {3}{2}}}{3 x^{6}}\) | \(13\) |
risch | \(-\frac {b \sqrt {b \,x^{2}}}{3 x^{4}}\) | \(14\) |
trager | \(\frac {b \left (x -1\right ) \left (x^{2}+x +1\right ) \sqrt {b \,x^{2}}}{3 x^{4}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 13, normalized size = 0.76 \begin {gather*} -\frac {\sqrt {b x^{2}} b}{3 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.29, size = 14, normalized size = 0.82 \begin {gather*} - \frac {\left (b x^{2}\right )^{\frac {3}{2}}}{3 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.64, size = 10, normalized size = 0.59 \begin {gather*} -\frac {b^{\frac {3}{2}} \mathrm {sgn}\left (x\right )}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.91, size = 10, normalized size = 0.59 \begin {gather*} -\frac {b^{3/2}}{3\,{\left (x^2\right )}^{3/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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