Optimal. Leaf size=56 \[ -\frac {250 (3 x+2)^{13}}{3159}+\frac {1025 (3 x+2)^{12}}{2916}-\frac {185}{891} (3 x+2)^{11}+\frac {107 (3 x+2)^{10}}{2430}-\frac {7 (3 x+2)^9}{2187} \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {250 (3 x+2)^{13}}{3159}+\frac {1025 (3 x+2)^{12}}{2916}-\frac {185}{891} (3 x+2)^{11}+\frac {107 (3 x+2)^{10}}{2430}-\frac {7 (3 x+2)^9}{2187} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx &=\int \left (-\frac {7}{81} (2+3 x)^8+\frac {107}{81} (2+3 x)^9-\frac {185}{27} (2+3 x)^{10}+\frac {1025}{81} (2+3 x)^{11}-\frac {250}{81} (2+3 x)^{12}\right ) \, dx\\ &=-\frac {7 (2+3 x)^9}{2187}+\frac {107 (2+3 x)^{10}}{2430}-\frac {185}{891} (2+3 x)^{11}+\frac {1025 (2+3 x)^{12}}{2916}-\frac {250 (2+3 x)^{13}}{3159}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 74, normalized size = 1.32 \begin {gather*} -\frac {1640250 x^{13}}{13}-\frac {3626775 x^{12}}{4}-\frac {32079645 x^{11}}{11}-\frac {54794799 x^{10}}{10}-6524829 x^9-4865076 x^8-1830960 x^7+350128 x^6+\frac {4580384 x^5}{5}+597824 x^4+224256 x^3+51840 x^2+6912 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.12, size = 64, normalized size = 1.14 \begin {gather*} -\frac {1640250}{13} x^{13} - \frac {3626775}{4} x^{12} - \frac {32079645}{11} x^{11} - \frac {54794799}{10} x^{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac {4580384}{5} x^{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.23, size = 64, normalized size = 1.14 \begin {gather*} -\frac {1640250}{13} \, x^{13} - \frac {3626775}{4} \, x^{12} - \frac {32079645}{11} \, x^{11} - \frac {54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac {4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 65, normalized size = 1.16 \begin {gather*} -\frac {1640250}{13} x^{13}-\frac {3626775}{4} x^{12}-\frac {32079645}{11} x^{11}-\frac {54794799}{10} x^{10}-6524829 x^{9}-4865076 x^{8}-1830960 x^{7}+350128 x^{6}+\frac {4580384}{5} x^{5}+597824 x^{4}+224256 x^{3}+51840 x^{2}+6912 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.52, size = 64, normalized size = 1.14 \begin {gather*} -\frac {1640250}{13} \, x^{13} - \frac {3626775}{4} \, x^{12} - \frac {32079645}{11} \, x^{11} - \frac {54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac {4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.08, size = 64, normalized size = 1.14 \begin {gather*} -\frac {1640250\,x^{13}}{13}-\frac {3626775\,x^{12}}{4}-\frac {32079645\,x^{11}}{11}-\frac {54794799\,x^{10}}{10}-6524829\,x^9-4865076\,x^8-1830960\,x^7+350128\,x^6+\frac {4580384\,x^5}{5}+597824\,x^4+224256\,x^3+51840\,x^2+6912\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 71, normalized size = 1.27 \begin {gather*} - \frac {1640250 x^{13}}{13} - \frac {3626775 x^{12}}{4} - \frac {32079645 x^{11}}{11} - \frac {54794799 x^{10}}{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac {4580384 x^{5}}{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________