Optimal. Leaf size=67 \[ \frac {100 (3 x+2)^{15}}{2187}-\frac {1900 (3 x+2)^{14}}{5103}+\frac {8285 (3 x+2)^{13}}{9477}-\frac {4099 (3 x+2)^{12}}{8748}+\frac {763 (3 x+2)^{11}}{8019}-\frac {49 (3 x+2)^{10}}{7290} \]
[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} \[ \frac {100 (3 x+2)^{15}}{2187}-\frac {1900 (3 x+2)^{14}}{5103}+\frac {8285 (3 x+2)^{13}}{9477}-\frac {4099 (3 x+2)^{12}}{8748}+\frac {763 (3 x+2)^{11}}{8019}-\frac {49 (3 x+2)^{10}}{7290} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^9+\frac {763}{243} (2+3 x)^{10}-\frac {4099}{243} (2+3 x)^{11}+\frac {8285}{243} (2+3 x)^{12}-\frac {3800}{243} (2+3 x)^{13}+\frac {500}{243} (2+3 x)^{14}\right ) \, dx\\ &=-\frac {49 (2+3 x)^{10}}{7290}+\frac {763 (2+3 x)^{11}}{8019}-\frac {4099 (2+3 x)^{12}}{8748}+\frac {8285 (2+3 x)^{13}}{9477}-\frac {1900 (2+3 x)^{14}}{5103}+\frac {100 (2+3 x)^{15}}{2187}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 90, normalized size = 1.34 \[ 656100 x^{15}+\frac {33461100 x^{14}}{7}+\frac {200077695 x^{13}}{13}+\frac {113029263 x^{12}}{4}+\frac {342976275 x^{11}}{11}+\frac {182657511 x^{10}}{10}-180666 x^9-9703638 x^8-\frac {55216512 x^7}{7}-\frac {7363312 x^6}{3}+\frac {2732864 x^5}{5}+871936 x^4+400128 x^3+100224 x^2+13824 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 74, normalized size = 1.10 \[ 656100 x^{15} + \frac {33461100}{7} x^{14} + \frac {200077695}{13} x^{13} + \frac {113029263}{4} x^{12} + \frac {342976275}{11} x^{11} + \frac {182657511}{10} x^{10} - 180666 x^{9} - 9703638 x^{8} - \frac {55216512}{7} x^{7} - \frac {7363312}{3} x^{6} + \frac {2732864}{5} x^{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.84, size = 74, normalized size = 1.10 \[ 656100 \, x^{15} + \frac {33461100}{7} \, x^{14} + \frac {200077695}{13} \, x^{13} + \frac {113029263}{4} \, x^{12} + \frac {342976275}{11} \, x^{11} + \frac {182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac {55216512}{7} \, x^{7} - \frac {7363312}{3} \, x^{6} + \frac {2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 75, normalized size = 1.12 \[ 656100 x^{15}+\frac {33461100}{7} x^{14}+\frac {200077695}{13} x^{13}+\frac {113029263}{4} x^{12}+\frac {342976275}{11} x^{11}+\frac {182657511}{10} x^{10}-180666 x^{9}-9703638 x^{8}-\frac {55216512}{7} x^{7}-\frac {7363312}{3} x^{6}+\frac {2732864}{5} x^{5}+871936 x^{4}+400128 x^{3}+100224 x^{2}+13824 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.47, size = 74, normalized size = 1.10 \[ 656100 \, x^{15} + \frac {33461100}{7} \, x^{14} + \frac {200077695}{13} \, x^{13} + \frac {113029263}{4} \, x^{12} + \frac {342976275}{11} \, x^{11} + \frac {182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac {55216512}{7} \, x^{7} - \frac {7363312}{3} \, x^{6} + \frac {2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.12, size = 74, normalized size = 1.10 \[ 656100\,x^{15}+\frac {33461100\,x^{14}}{7}+\frac {200077695\,x^{13}}{13}+\frac {113029263\,x^{12}}{4}+\frac {342976275\,x^{11}}{11}+\frac {182657511\,x^{10}}{10}-180666\,x^9-9703638\,x^8-\frac {55216512\,x^7}{7}-\frac {7363312\,x^6}{3}+\frac {2732864\,x^5}{5}+871936\,x^4+400128\,x^3+100224\,x^2+13824\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 87, normalized size = 1.30 \[ 656100 x^{15} + \frac {33461100 x^{14}}{7} + \frac {200077695 x^{13}}{13} + \frac {113029263 x^{12}}{4} + \frac {342976275 x^{11}}{11} + \frac {182657511 x^{10}}{10} - 180666 x^{9} - 9703638 x^{8} - \frac {55216512 x^{7}}{7} - \frac {7363312 x^{6}}{3} + \frac {2732864 x^{5}}{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________