Optimal. Leaf size=28 \[ -\frac {3 \left (a+b x^2\right )^{7/3}}{14 a c (c x)^{14/3}} \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {264} \[ -\frac {3 \left (a+b x^2\right )^{7/3}}{14 a c (c x)^{14/3}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^{4/3}}{(c x)^{17/3}} \, dx &=-\frac {3 \left (a+b x^2\right )^{7/3}}{14 a c (c x)^{14/3}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 0.93 \[ -\frac {3 x \left (a+b x^2\right )^{7/3}}{14 a (c x)^{17/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.17, size = 43, normalized size = 1.54 \[ -\frac {3 \, {\left (b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right )} {\left (b x^{2} + a\right )}^{\frac {1}{3}} \left (c x\right )^{\frac {1}{3}}}{14 \, a c^{6} x^{5}} \]
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 \[ \int \frac {{\left (b x^{2} + a\right )}^{\frac {4}{3}}}{\left (c x\right )^{\frac {17}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 0.75 \[ -\frac {3 \left (b \,x^{2}+a \right )^{\frac {7}{3}} x}{14 \left (c x \right )^{\frac {17}{3}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b x^{2} + a\right )}^{\frac {4}{3}}}{\left (c x\right )^{\frac {17}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (b\,x^2+a\right )}^{4/3}}{{\left (c\,x\right )}^{17/3}} \,d x \]
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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