Optimal. Leaf size=17 \[ \frac {1}{2} b^2 x \sqrt {b x^2} \]
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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 {1}{2} b^2 x \sqrt {b x^2} \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 )^{5/2}}{x^4} \, dx &=\frac {\left (b^2 \sqrt {b x^2}\right ) \int x \, dx}{x}\\ &=\frac {1}{2} b^2 x \sqrt {b x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {1}{2} b^2 x \sqrt {b x^2} \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 | \(\frac {\left (b \,x^{2}\right )^{\frac {5}{2}}}{2 x^{3}}\) | \(13\) |
default | \(\frac {\left (b \,x^{2}\right )^{\frac {5}{2}}}{2 x^{3}}\) | \(13\) |
risch | \(\frac {b^{2} x \sqrt {b \,x^{2}}}{2}\) | \(14\) |
trager | \(\frac {b^{2} \left (x -1\right ) \left (x +1\right ) \sqrt {b \,x^{2}}}{2 x}\) | \(22\) |
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 {1}{2} \, \sqrt {b x^{2}} b^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.29, size = 12, normalized size = 0.71 \begin {gather*} \frac {\left (b x^{2}\right )^{\frac {5}{2}}}{2 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.46, size = 10, normalized size = 0.59 \begin {gather*} \frac {1}{2} \, b^{\frac {5}{2}} x^{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 = 0.94, size = 8, normalized size = 0.47 \begin {gather*} \frac {b^{5/2}\,x\,\left |x\right |}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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