Optimal. Leaf size=67 \[ -\frac {49 (2+3 x)^6}{4374}+\frac {109}{729} (2+3 x)^7-\frac {4099 (2+3 x)^8}{5832}+\frac {8285 (2+3 x)^9}{6561}-\frac {380}{729} (2+3 x)^{10}+\frac {500 (2+3 x)^{11}}{8019} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, 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 = {90}
\begin {gather*} \frac {500 (3 x+2)^{11}}{8019}-\frac {380}{729} (3 x+2)^{10}+\frac {8285 (3 x+2)^9}{6561}-\frac {4099 (3 x+2)^8}{5832}+\frac {109}{729} (3 x+2)^7-\frac {49 (3 x+2)^6}{4374} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^5+\frac {763}{243} (2+3 x)^6-\frac {4099}{243} (2+3 x)^7+\frac {8285}{243} (2+3 x)^8-\frac {3800}{243} (2+3 x)^9+\frac {500}{243} (2+3 x)^{10}\right ) \, dx\\ &=-\frac {49 (2+3 x)^6}{4374}+\frac {109}{729} (2+3 x)^7-\frac {4099 (2+3 x)^8}{5832}+\frac {8285 (2+3 x)^9}{6561}-\frac {380}{729} (2+3 x)^{10}+\frac {500 (2+3 x)^{11}}{8019}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 60, normalized size = 0.90 \begin {gather*} 864 x+3672 x^2+6432 x^3-2150 x^4-28322 x^5-\frac {252329 x^6}{6}-987 x^7+\frac {551349 x^8}{8}+89655 x^9+50220 x^{10}+\frac {121500 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 55, normalized size = 0.82
method | result | size |
gosper | \(\frac {x \left (2916000 x^{10}+13258080 x^{9}+23668920 x^{8}+18194517 x^{7}-260568 x^{6}-11102476 x^{5}-7477008 x^{4}-567600 x^{3}+1698048 x^{2}+969408 x +228096\right )}{264}\) | \(54\) |
default | \(\frac {121500}{11} x^{11}+50220 x^{10}+89655 x^{9}+\frac {551349}{8} x^{8}-987 x^{7}-\frac {252329}{6} x^{6}-28322 x^{5}-2150 x^{4}+6432 x^{3}+3672 x^{2}+864 x\) | \(55\) |
norman | \(\frac {121500}{11} x^{11}+50220 x^{10}+89655 x^{9}+\frac {551349}{8} x^{8}-987 x^{7}-\frac {252329}{6} x^{6}-28322 x^{5}-2150 x^{4}+6432 x^{3}+3672 x^{2}+864 x\) | \(55\) |
risch | \(\frac {121500}{11} x^{11}+50220 x^{10}+89655 x^{9}+\frac {551349}{8} x^{8}-987 x^{7}-\frac {252329}{6} x^{6}-28322 x^{5}-2150 x^{4}+6432 x^{3}+3672 x^{2}+864 x\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 54, normalized size = 0.81 \begin {gather*} \frac {121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac {551349}{8} \, x^{8} - 987 \, x^{7} - \frac {252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.40, size = 54, normalized size = 0.81 \begin {gather*} \frac {121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac {551349}{8} \, x^{8} - 987 \, x^{7} - \frac {252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 58, normalized size = 0.87 \begin {gather*} \frac {121500 x^{11}}{11} + 50220 x^{10} + 89655 x^{9} + \frac {551349 x^{8}}{8} - 987 x^{7} - \frac {252329 x^{6}}{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.19, size = 54, normalized size = 0.81 \begin {gather*} \frac {121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac {551349}{8} \, x^{8} - 987 \, x^{7} - \frac {252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.05, size = 54, normalized size = 0.81 \begin {gather*} \frac {121500\,x^{11}}{11}+50220\,x^{10}+89655\,x^9+\frac {551349\,x^8}{8}-987\,x^7-\frac {252329\,x^6}{6}-28322\,x^5-2150\,x^4+6432\,x^3+3672\,x^2+864\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________