Integrand size = 33, antiderivative size = 55 \[ \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx=-\frac {45 x^{43/15}}{43}+\frac {360 x^{37/10}}{37}+\frac {60 x^{113/30}}{113}-\frac {120 x^{23/5}}{23}-\frac {x^{14/3}}{14}+\frac {8 x^{11/2}}{11} \]
[Out]
Time = 0.19 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1607, 1598, 1834} \[ \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx=\frac {8 x^{11/2}}{11}-\frac {x^{14/3}}{14}-\frac {120 x^{23/5}}{23}+\frac {60 x^{113/30}}{113}+\frac {360 x^{37/10}}{37}-\frac {45 x^{43/15}}{43} \]
[In]
[Out]
Rule 1598
Rule 1607
Rule 1834
Rubi steps \begin{align*} \text {integral}& = \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 \text {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 \text {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*}
Time = 0.19 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.00 \[ \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx=-\frac {45 x^{43/15}}{43}+\frac {360 x^{37/10}}{37}+\frac {60 x^{113/30}}{113}-\frac {120 x^{23/5}}{23}-\frac {x^{14/3}}{14}+\frac {8 x^{11/2}}{11} \]
[In]
[Out]
Time = 0.22 (sec) , antiderivative size = 32, normalized size of antiderivative = 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 | \(-\frac {45 x^{\frac {43}{15}}}{43}+\frac {360 x^{\frac {37}{10}}}{37}+\frac {60 x^{\frac {113}{30}}}{113}-\frac {120 x^{\frac {23}{5}}}{23}-\frac {x^{\frac {14}{3}}}{14}+\frac {8 x^{\frac {11}{2}}}{11}\) | \(32\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.56 \[ \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx=\frac {8}{11} \, x^{\frac {11}{2}} - \frac {1}{14} \, x^{\frac {14}{3}} - \frac {120}{23} \, x^{\frac {23}{5}} + \frac {60}{113} \, x^{\frac {113}{30}} + \frac {360}{37} \, x^{\frac {37}{10}} - \frac {45}{43} \, x^{\frac {43}{15}} \]
[In]
[Out]
Time = 1.21 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.87 \[ \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx=\frac {60 x^{\frac {113}{30}}}{113} - \frac {45 x^{\frac {43}{15}}}{43} + \frac {360 x^{\frac {37}{10}}}{37} - \frac {120 x^{\frac {23}{5}}}{23} - \frac {x^{\frac {14}{3}}}{14} + \frac {8 x^{\frac {11}{2}}}{11} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.56 \[ \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx=\frac {8}{11} \, x^{\frac {11}{2}} - \frac {1}{14} \, x^{\frac {14}{3}} - \frac {120}{23} \, x^{\frac {23}{5}} + \frac {60}{113} \, x^{\frac {113}{30}} + \frac {360}{37} \, x^{\frac {37}{10}} - \frac {45}{43} \, x^{\frac {43}{15}} \]
[In]
[Out]
none
Time = 0.31 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.56 \[ \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx=\frac {8}{11} \, x^{\frac {11}{2}} - \frac {1}{14} \, x^{\frac {14}{3}} - \frac {120}{23} \, x^{\frac {23}{5}} + \frac {60}{113} \, x^{\frac {113}{30}} + \frac {360}{37} \, x^{\frac {37}{10}} - \frac {45}{43} \, x^{\frac {43}{15}} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.56 \[ \int \left (-3 x^{3/5}+x^{3/2}\right )^2 \left (-\frac {x^{2/3}}{3}+4 x^{3/2}\right ) \, dx=\frac {8\,x^{11/2}}{11}-\frac {x^{14/3}}{14}-\frac {120\,x^{23/5}}{23}+\frac {360\,x^{37/10}}{37}-\frac {45\,x^{43/15}}{43}+\frac {60\,x^{113/30}}{113} \]
[In]
[Out]