Optimal. Leaf size=55 \[ \frac {8 x^{11/2}}{11}-\frac {x^{14/3}}{14}-\frac {120 x^{23/5}}{23}+\frac {60 x^{113/30}}{113}+\frac {360 x^{37/10}}{37}-\frac {45 x^{43/15}}{43} \]
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Rubi [A] time = 0.24, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1593, 1584, 1820} \[ \frac {8 x^{11/2}}{11}-\frac {x^{14/3}}{14}-\frac {120 x^{23/5}}{23}+\frac {60 x^{113/30}}{113}+\frac {360 x^{37/10}}{37}-\frac {45 x^{43/15}}{43} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 1593
Rule 1820
Rubi steps
\begin {align*} \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx &=\int \left (-3+x^{9/10}\right )^2 x^{6/5} \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx\\ &=\int \left (-\frac {1}{3}+4 x^{5/6}\right ) \left (-3+x^{9/10}\right )^2 x^{28/15} \, dx\\ &=30 \operatorname {Subst}\left (\int x^{85} \left (-\frac {1}{3}+4 x^{25}\right ) \left (-3+x^{27}\right )^2 \, dx,x,\sqrt [30]{x}\right )\\ &=30 \operatorname {Subst}\left (\int \left (-3 x^{85}+36 x^{110}+2 x^{112}-24 x^{137}-\frac {x^{139}}{3}+4 x^{164}\right ) \, dx,x,\sqrt [30]{x}\right )\\ &=-\frac {45 x^{43/15}}{43}+\frac {360 x^{37/10}}{37}+\frac {60 x^{113/30}}{113}-\frac {120 x^{23/5}}{23}-\frac {x^{14/3}}{14}+\frac {8 x^{11/2}}{11}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 55, normalized size = 1.00 \[ \frac {8 x^{11/2}}{11}-\frac {x^{14/3}}{14}-\frac {120 x^{23/5}}{23}+\frac {60 x^{113/30}}{113}+\frac {360 x^{37/10}}{37}-\frac {45 x^{43/15}}{43} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 55, normalized size = 1.00 \[ \frac {8 x^{11/2}}{11}-\frac {x^{14/3}}{14}-\frac {120 x^{23/5}}{23}+\frac {60 x^{113/30}}{113}+\frac {360 x^{37/10}}{37}-\frac {45 x^{43/15}}{43} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.18, size = 31, normalized size = 0.56 \[ \frac {8}{11} \, x^{\frac {11}{2}} - \frac {1}{14} \, x^{\frac {14}{3}} - \frac {120}{23} \, x^{\frac {23}{5}} + \frac {60}{113} \, x^{\frac {113}{30}} + \frac {360}{37} \, x^{\frac {37}{10}} - \frac {45}{43} \, x^{\frac {43}{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 31, normalized size = 0.56 \[ \frac {8}{11} \, x^{\frac {11}{2}} - \frac {1}{14} \, x^{\frac {14}{3}} - \frac {120}{23} \, x^{\frac {23}{5}} + \frac {60}{113} \, x^{\frac {113}{30}} + \frac {360}{37} \, x^{\frac {37}{10}} - \frac {45}{43} \, x^{\frac {43}{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 32, normalized size = 0.58
method | result | size |
derivativedivides | \(-\frac {45 x^{\frac {43}{15}}}{43}+\frac {360 x^{\frac {37}{10}}}{37}+\frac {60 x^{\frac {113}{30}}}{113}-\frac {120 x^{\frac {23}{5}}}{23}-\frac {x^{\frac {14}{3}}}{14}+\frac {8 x^{\frac {11}{2}}}{11}\) | \(32\) |
default | \(-\frac {45 x^{\frac {43}{15}}}{43}+\frac {360 x^{\frac {37}{10}}}{37}+\frac {60 x^{\frac {113}{30}}}{113}-\frac {120 x^{\frac {23}{5}}}{23}-\frac {x^{\frac {14}{3}}}{14}+\frac {8 x^{\frac {11}{2}}}{11}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 31, normalized size = 0.56 \[ \frac {8}{11} \, x^{\frac {11}{2}} - \frac {1}{14} \, x^{\frac {14}{3}} - \frac {120}{23} \, x^{\frac {23}{5}} + \frac {60}{113} \, x^{\frac {113}{30}} + \frac {360}{37} \, x^{\frac {37}{10}} - \frac {45}{43} \, x^{\frac {43}{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 31, normalized size = 0.56 \[ \frac {8\,x^{11/2}}{11}-\frac {x^{14/3}}{14}-\frac {120\,x^{23/5}}{23}+\frac {360\,x^{37/10}}{37}-\frac {45\,x^{43/15}}{43}+\frac {60\,x^{113/30}}{113} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.75, size = 48, normalized size = 0.87 \[ \frac {60 x^{\frac {113}{30}}}{113} - \frac {45 x^{\frac {43}{15}}}{43} + \frac {360 x^{\frac {37}{10}}}{37} - \frac {120 x^{\frac {23}{5}}}{23} - \frac {x^{\frac {14}{3}}}{14} + \frac {8 x^{\frac {11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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