Optimal. Leaf size=21 \[ \frac {2 x^3}{(6-n) \sqrt {b x^n}} \]
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Rubi [A]
time = 0.00, antiderivative size = 21, 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 {2 x^3}{(6-n) \sqrt {b x^n}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {x^2}{\sqrt {b x^n}} \, dx &=\frac {x^{n/2} \int x^{2-\frac {n}{2}} \, dx}{\sqrt {b x^n}}\\ &=\frac {2 x^3}{(6-n) \sqrt {b x^n}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 0.90 \begin {gather*} -\frac {2 x^3}{(-6+n) \sqrt {b x^n}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 18, normalized size = 0.86
method | result | size |
gosper | \(-\frac {2 x^{3}}{\left (-6+n \right ) \sqrt {b \,x^{n}}}\) | \(18\) |
risch | \(-\frac {2 x^{3}}{\left (-6+n \right ) \sqrt {b \,x^{n}}}\) | \(18\) |
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: ValueError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \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*} \begin {cases} - \frac {2 x^{3}}{n \sqrt {b x^{n}} - 6 \sqrt {b x^{n}}} & \text {for}\: n \neq 6 \\\int \frac {x^{2}}{\sqrt {b x^{6}}}\, dx & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.04, size = 24, normalized size = 1.14 \begin {gather*} -\frac {2\,x^{3-n}\,\sqrt {b\,x^n}}{b\,\left (n-6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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