Optimal. Leaf size=16 \[ \frac {b \sqrt {b x^2} \log (x)}{x} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, 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, 29}
\begin {gather*} \frac {b \sqrt {b x^2} \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin {align*} \int \frac {\left (b x^2\right )^{3/2}}{x^4} \, dx &=\frac {\left (b \sqrt {b x^2}\right ) \int \frac {1}{x} \, dx}{x}\\ &=\frac {b \sqrt {b x^2} \log (x)}{x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} \frac {\left (b x^2\right )^{3/2} \log (x)}{x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.88
method | result | size |
default | \(\frac {\left (b \,x^{2}\right )^{\frac {3}{2}} \ln \left (x \right )}{x^{3}}\) | \(14\) |
risch | \(\frac {b \ln \left (x \right ) \sqrt {b \,x^{2}}}{x}\) | \(15\) |
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 = 0.35, size = 14, normalized size = 0.88 \begin {gather*} \frac {\sqrt {b x^{2}} b \log \left (x\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (b x^{2}\right )^{\frac {3}{2}}}{x^{4}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.81, size = 9, normalized size = 0.56 \begin {gather*} b^{\frac {3}{2}} \log \left ({\left | x \right |}\right ) \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 = -0.06 \begin {gather*} \int \frac {{\left (b\,x^2\right )}^{3/2}}{x^4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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