Optimal. Leaf size=16 \[ \frac {x^2}{b \sqrt {b x^2}} \]
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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, 8}
\begin {gather*} \frac {x^2}{b \sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 15
Rubi steps
\begin {align*} \int \frac {x^3}{\left (b x^2\right )^{3/2}} \, dx &=\frac {x \int 1 \, dx}{b \sqrt {b x^2}}\\ &=\frac {x^2}{b \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 0.81 \begin {gather*} \frac {x^4}{\left (b x^2\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 12, normalized size = 0.75
method | result | size |
default | \(\frac {x^{4}}{\left (b \,x^{2}\right )^{\frac {3}{2}}}\) | \(12\) |
risch | \(\frac {x^{2}}{b \sqrt {b \,x^{2}}}\) | \(15\) |
trager | \(\frac {\left (x -1\right ) \sqrt {b \,x^{2}}}{b^{2} x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 14, normalized size = 0.88 \begin {gather*} \frac {x^{2}}{\sqrt {b x^{2}} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 11, normalized size = 0.69 \begin {gather*} \frac {\sqrt {b x^{2}}}{b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.20, size = 10, normalized size = 0.62 \begin {gather*} \frac {x^{4}}{\left (b x^{2}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.84, size = 9, normalized size = 0.56 \begin {gather*} \frac {x}{b^{\frac {3}{2}} \mathrm {sgn}\left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.99, size = 6, normalized size = 0.38 \begin {gather*} \frac {\left |x\right |}{b^{3/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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