Optimal. Leaf size=45 \[ \frac {20}{891} (3 x+2)^{11}-\frac {8}{45} (3 x+2)^{10}+\frac {91}{243} (3 x+2)^9-\frac {49}{648} (3 x+2)^8 \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 45, 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 {20}{891} (3 x+2)^{11}-\frac {8}{45} (3 x+2)^{10}+\frac {91}{243} (3 x+2)^9-\frac {49}{648} (3 x+2)^8 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx &=\int \left (-\frac {49}{27} (2+3 x)^7+\frac {91}{9} (2+3 x)^8-\frac {16}{3} (2+3 x)^9+\frac {20}{27} (2+3 x)^{10}\right ) \, dx\\ &=-\frac {49}{648} (2+3 x)^8+\frac {91}{243} (2+3 x)^9-\frac {8}{45} (2+3 x)^{10}+\frac {20}{891} (2+3 x)^{11}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 64, normalized size = 1.42 \begin {gather*} \frac {43740 x^{11}}{11}+\frac {93312 x^{10}}{5}+34587 x^9+\frac {225423 x^8}{8}+1242 x^7-16254 x^6-\frac {59304 x^5}{5}-1292 x^4+\frac {7712 x^3}{3}+1568 x^2+384 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 (2+3 x)^7 (3+5 x) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.15, size = 54, normalized size = 1.20 \begin {gather*} \frac {43740}{11} x^{11} + \frac {93312}{5} x^{10} + 34587 x^{9} + \frac {225423}{8} x^{8} + 1242 x^{7} - 16254 x^{6} - \frac {59304}{5} x^{5} - 1292 x^{4} + \frac {7712}{3} x^{3} + 1568 x^{2} + 384 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.15, size = 54, normalized size = 1.20 \begin {gather*} \frac {43740}{11} \, x^{11} + \frac {93312}{5} \, x^{10} + 34587 \, x^{9} + \frac {225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac {59304}{5} \, x^{5} - 1292 \, x^{4} + \frac {7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 55, normalized size = 1.22 \begin {gather*} \frac {43740}{11} x^{11}+\frac {93312}{5} x^{10}+34587 x^{9}+\frac {225423}{8} x^{8}+1242 x^{7}-16254 x^{6}-\frac {59304}{5} x^{5}-1292 x^{4}+\frac {7712}{3} x^{3}+1568 x^{2}+384 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 54, normalized size = 1.20 \begin {gather*} \frac {43740}{11} \, x^{11} + \frac {93312}{5} \, x^{10} + 34587 \, x^{9} + \frac {225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac {59304}{5} \, x^{5} - 1292 \, x^{4} + \frac {7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 54, normalized size = 1.20 \begin {gather*} \frac {43740\,x^{11}}{11}+\frac {93312\,x^{10}}{5}+34587\,x^9+\frac {225423\,x^8}{8}+1242\,x^7-16254\,x^6-\frac {59304\,x^5}{5}-1292\,x^4+\frac {7712\,x^3}{3}+1568\,x^2+384\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 61, normalized size = 1.36 \begin {gather*} \frac {43740 x^{11}}{11} + \frac {93312 x^{10}}{5} + 34587 x^{9} + \frac {225423 x^{8}}{8} + 1242 x^{7} - 16254 x^{6} - \frac {59304 x^{5}}{5} - 1292 x^{4} + \frac {7712 x^{3}}{3} + 1568 x^{2} + 384 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________