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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IntegrateAlgebraic [A] time = 0.01, size = 16, normalized size = 0.94 \begin {gather*} -\frac {b^3}{3 \left (b x^2\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.98, 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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giac [A] time = 0.16, size = 10, normalized size = 0.59 \begin {gather*} -\frac {b^{\frac {3}{2}} \mathrm {sgn}\relax (x)}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.76 \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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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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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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sympy [A] time = 1.29, size = 17, normalized size = 1.00 \begin {gather*} - \frac {b^{\frac {3}{2}} \left (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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