Optimal. Leaf size=67 \[ -\frac {50 (3 x+2)^{12}}{2187}+\frac {2180 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{3645}+\frac {11599 (3 x+2)^9}{6561}-\frac {931 (3 x+2)^8}{1458}+\frac {49}{729} (3 x+2)^7 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 67, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ -\frac {50 (3 x+2)^{12}}{2187}+\frac {2180 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{3645}+\frac {11599 (3 x+2)^9}{6561}-\frac {931 (3 x+2)^8}{1458}+\frac {49}{729} (3 x+2)^7 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx &=\int \left (\frac {343}{243} (2+3 x)^6-\frac {3724}{243} (2+3 x)^7+\frac {11599}{243} (2+3 x)^8-\frac {8198}{243} (2+3 x)^9+\frac {2180}{243} (2+3 x)^{10}-\frac {200}{243} (2+3 x)^{11}\right ) \, dx\\ &=\frac {49}{729} (2+3 x)^7-\frac {931 (2+3 x)^8}{1458}+\frac {11599 (2+3 x)^9}{6561}-\frac {4099 (2+3 x)^{10}}{3645}+\frac {2180 (2+3 x)^{11}}{8019}-\frac {50 (2+3 x)^{12}}{2187}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 71, normalized size = 1.06 \[ -12150 x^{12}-\frac {539460 x^{11}}{11}-\frac {348219 x^{10}}{5}-22695 x^9+\frac {85833 x^8}{2}+45531 x^7+\frac {13202 x^6}{3}-\frac {78132 x^5}{5}-7800 x^4+\frac {2608 x^3}{3}+1824 x^2+576 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 59, normalized size = 0.88 \[ -12150 x^{12} - \frac {539460}{11} x^{11} - \frac {348219}{5} x^{10} - 22695 x^{9} + \frac {85833}{2} x^{8} + 45531 x^{7} + \frac {13202}{3} x^{6} - \frac {78132}{5} x^{5} - 7800 x^{4} + \frac {2608}{3} x^{3} + 1824 x^{2} + 576 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.95, size = 59, normalized size = 0.88 \[ -12150 \, x^{12} - \frac {539460}{11} \, x^{11} - \frac {348219}{5} \, x^{10} - 22695 \, x^{9} + \frac {85833}{2} \, x^{8} + 45531 \, x^{7} + \frac {13202}{3} \, x^{6} - \frac {78132}{5} \, x^{5} - 7800 \, x^{4} + \frac {2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 60, normalized size = 0.90 \[ -12150 x^{12}-\frac {539460}{11} x^{11}-\frac {348219}{5} x^{10}-22695 x^{9}+\frac {85833}{2} x^{8}+45531 x^{7}+\frac {13202}{3} x^{6}-\frac {78132}{5} x^{5}-7800 x^{4}+\frac {2608}{3} x^{3}+1824 x^{2}+576 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 59, normalized size = 0.88 \[ -12150 \, x^{12} - \frac {539460}{11} \, x^{11} - \frac {348219}{5} \, x^{10} - 22695 \, x^{9} + \frac {85833}{2} \, x^{8} + 45531 \, x^{7} + \frac {13202}{3} \, x^{6} - \frac {78132}{5} \, x^{5} - 7800 \, x^{4} + \frac {2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 59, normalized size = 0.88 \[ -12150\,x^{12}-\frac {539460\,x^{11}}{11}-\frac {348219\,x^{10}}{5}-22695\,x^9+\frac {85833\,x^8}{2}+45531\,x^7+\frac {13202\,x^6}{3}-\frac {78132\,x^5}{5}-7800\,x^4+\frac {2608\,x^3}{3}+1824\,x^2+576\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 68, normalized size = 1.01 \[ - 12150 x^{12} - \frac {539460 x^{11}}{11} - \frac {348219 x^{10}}{5} - 22695 x^{9} + \frac {85833 x^{8}}{2} + 45531 x^{7} + \frac {13202 x^{6}}{3} - \frac {78132 x^{5}}{5} - 7800 x^{4} + \frac {2608 x^{3}}{3} + 1824 x^{2} + 576 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________