Optimal. Leaf size=19 \[ \frac {3 x}{(3-n) \sqrt [3]{b x^n}} \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac {3 x}{(3-n) \sqrt [3]{b x^n}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\sqrt [3]{b x^n}} \, dx &=\frac {x^{n/3} \int x^{-n/3} \, dx}{\sqrt [3]{b x^n}}\\ &=\frac {3 x}{(3-n) \sqrt [3]{b x^n}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.89 \[ -\frac {3 x}{(n-3) \sqrt [3]{b x^n}} \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
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 \[ \int \frac {1}{\left (b x^{n}\right )^{\frac {1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.84 \[ -\frac {3 x}{\left (n -3\right ) \left (b \,x^{n}\right )^{\frac {1}{3}}} \]
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 \[ \text {Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.98, size = 24, normalized size = 1.26 \[ -\frac {3\,x^{1-n}\,{\left (b\,x^n\right )}^{2/3}}{b\,\left (n-3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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