Optimal. Leaf size=93 \[ \frac {891 x}{1820 a^4 \sqrt [3]{a+b x^3}}+\frac {297 x}{1820 a^3 \left (a+b x^3\right )^{4/3}}+\frac {99 x}{910 a^2 \left (a+b x^3\right )^{7/3}}+\frac {11 x}{130 a \left (a+b x^3\right )^{10/3}}+\frac {2 x}{13 \left (a+b x^3\right )^{13/3}} \]
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Rubi [A] time = 0.03, antiderivative size = 93, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {385, 192, 191} \[ \frac {891 x}{1820 a^4 \sqrt [3]{a+b x^3}}+\frac {297 x}{1820 a^3 \left (a+b x^3\right )^{4/3}}+\frac {99 x}{910 a^2 \left (a+b x^3\right )^{7/3}}+\frac {11 x}{130 a \left (a+b x^3\right )^{10/3}}+\frac {2 x}{13 \left (a+b x^3\right )^{13/3}} \]
Antiderivative was successfully verified.
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Rule 191
Rule 192
Rule 385
Rubi steps
\begin {align*} \int \frac {a-b x^3}{\left (a+b x^3\right )^{16/3}} \, dx &=\frac {2 x}{13 \left (a+b x^3\right )^{13/3}}+\frac {11}{13} \int \frac {1}{\left (a+b x^3\right )^{13/3}} \, dx\\ &=\frac {2 x}{13 \left (a+b x^3\right )^{13/3}}+\frac {11 x}{130 a \left (a+b x^3\right )^{10/3}}+\frac {99 \int \frac {1}{\left (a+b x^3\right )^{10/3}} \, dx}{130 a}\\ &=\frac {2 x}{13 \left (a+b x^3\right )^{13/3}}+\frac {11 x}{130 a \left (a+b x^3\right )^{10/3}}+\frac {99 x}{910 a^2 \left (a+b x^3\right )^{7/3}}+\frac {297 \int \frac {1}{\left (a+b x^3\right )^{7/3}} \, dx}{455 a^2}\\ &=\frac {2 x}{13 \left (a+b x^3\right )^{13/3}}+\frac {11 x}{130 a \left (a+b x^3\right )^{10/3}}+\frac {99 x}{910 a^2 \left (a+b x^3\right )^{7/3}}+\frac {297 x}{1820 a^3 \left (a+b x^3\right )^{4/3}}+\frac {891 \int \frac {1}{\left (a+b x^3\right )^{4/3}} \, dx}{1820 a^3}\\ &=\frac {2 x}{13 \left (a+b x^3\right )^{13/3}}+\frac {11 x}{130 a \left (a+b x^3\right )^{10/3}}+\frac {99 x}{910 a^2 \left (a+b x^3\right )^{7/3}}+\frac {297 x}{1820 a^3 \left (a+b x^3\right )^{4/3}}+\frac {891 x}{1820 a^4 \sqrt [3]{a+b x^3}}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 62, normalized size = 0.67 \[ \frac {x \left (1820 a^4+5005 a^3 b x^3+6435 a^2 b^2 x^6+3861 a b^3 x^9+891 b^4 x^{12}\right )}{1820 a^4 \left (a+b x^3\right )^{13/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 113, normalized size = 1.22 \[ \frac {{\left (891 \, b^{4} x^{13} + 3861 \, a b^{3} x^{10} + 6435 \, a^{2} b^{2} x^{7} + 5005 \, a^{3} b x^{4} + 1820 \, a^{4} x\right )} {\left (b x^{3} + a\right )}^{\frac {2}{3}}}{1820 \, {\left (a^{4} b^{5} x^{15} + 5 \, a^{5} b^{4} x^{12} + 10 \, a^{6} b^{3} x^{9} + 10 \, a^{7} b^{2} x^{6} + 5 \, a^{8} b x^{3} + a^{9}\right )}} \]
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 \[ \int -\frac {b x^{3} - a}{{\left (b x^{3} + a\right )}^{\frac {16}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 59, normalized size = 0.63 \[ \frac {\left (891 b^{4} x^{12}+3861 b^{3} x^{9} a +6435 b^{2} x^{6} a^{2}+5005 b \,x^{3} a^{3}+1820 a^{4}\right ) x}{1820 \left (b \,x^{3}+a \right )^{\frac {13}{3}} a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 153, normalized size = 1.65 \[ \frac {{\left (140 \, b^{3} - \frac {546 \, {\left (b x^{3} + a\right )} b^{2}}{x^{3}} + \frac {780 \, {\left (b x^{3} + a\right )}^{2} b}{x^{6}} - \frac {455 \, {\left (b x^{3} + a\right )}^{3}}{x^{9}}\right )} b x^{13}}{1820 \, {\left (b x^{3} + a\right )}^{\frac {13}{3}} a^{4}} + \frac {{\left (35 \, b^{4} - \frac {182 \, {\left (b x^{3} + a\right )} b^{3}}{x^{3}} + \frac {390 \, {\left (b x^{3} + a\right )}^{2} b^{2}}{x^{6}} - \frac {455 \, {\left (b x^{3} + a\right )}^{3} b}{x^{9}} + \frac {455 \, {\left (b x^{3} + a\right )}^{4}}{x^{12}}\right )} x^{13}}{455 \, {\left (b x^{3} + a\right )}^{\frac {13}{3}} a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.37, size = 73, normalized size = 0.78 \[ \frac {2\,x}{13\,{\left (b\,x^3+a\right )}^{13/3}}+\frac {891\,x}{1820\,a^4\,{\left (b\,x^3+a\right )}^{1/3}}+\frac {297\,x}{1820\,a^3\,{\left (b\,x^3+a\right )}^{4/3}}+\frac {99\,x}{910\,a^2\,{\left (b\,x^3+a\right )}^{7/3}}+\frac {11\,x}{130\,a\,{\left (b\,x^3+a\right )}^{10/3}} \]
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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