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} \[ \frac {b \sqrt {b x^2} \log (x)}{x} \]
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 \[ \frac {\left (b x^2\right )^{3/2} \log (x)}{x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 14, normalized size = 0.88 \[ \frac {\sqrt {b x^{2}} b \log \relax (x)}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 9, normalized size = 0.56 \[ b^{\frac {3}{2}} \log \left ({\left | x \right |}\right ) \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.88 \[ \frac {\left (b \,x^{2}\right )^{\frac {3}{2}} \ln \relax (x )}{x^{3}} \]
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 \[ \text {Exception raised: RuntimeError} \]
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 \[ \int \frac {{\left (b\,x^2\right )}^{3/2}}{x^4} \,d x \]
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 \[ \int \frac {\left (b x^{2}\right )^{\frac {3}{2}}}{x^{4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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