Optimal. Leaf size=45 \[ -135 x^8-\frac {1188 x^7}{7}+111 x^6+\frac {949 x^5}{5}-\frac {117 x^4}{4}-86 x^3+2 x^2+24 x \]
________________________________________________________________________________________
Rubi [A] time = 0.02, 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*} -135 x^8-\frac {1188 x^7}{7}+111 x^6+\frac {949 x^5}{5}-\frac {117 x^4}{4}-86 x^3+2 x^2+24 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx &=\int \left (24+4 x-258 x^2-117 x^3+949 x^4+666 x^5-1188 x^6-1080 x^7\right ) \, dx\\ &=24 x+2 x^2-86 x^3-\frac {117 x^4}{4}+\frac {949 x^5}{5}+111 x^6-\frac {1188 x^7}{7}-135 x^8\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 45, normalized size = 1.00 \begin {gather*} -135 x^8-\frac {1188 x^7}{7}+111 x^6+\frac {949 x^5}{5}-\frac {117 x^4}{4}-86 x^3+2 x^2+24 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)^3 (2+3 x)^3 (3+5 x) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.80, size = 39, normalized size = 0.87 \begin {gather*} -135 x^{8} - \frac {1188}{7} x^{7} + 111 x^{6} + \frac {949}{5} x^{5} - \frac {117}{4} x^{4} - 86 x^{3} + 2 x^{2} + 24 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.01, size = 39, normalized size = 0.87 \begin {gather*} -135 \, x^{8} - \frac {1188}{7} \, x^{7} + 111 \, x^{6} + \frac {949}{5} \, x^{5} - \frac {117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 40, normalized size = 0.89 \begin {gather*} -135 x^{8}-\frac {1188}{7} x^{7}+111 x^{6}+\frac {949}{5} x^{5}-\frac {117}{4} x^{4}-86 x^{3}+2 x^{2}+24 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.61, size = 39, normalized size = 0.87 \begin {gather*} -135 \, x^{8} - \frac {1188}{7} \, x^{7} + 111 \, x^{6} + \frac {949}{5} \, x^{5} - \frac {117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 39, normalized size = 0.87 \begin {gather*} -135\,x^8-\frac {1188\,x^7}{7}+111\,x^6+\frac {949\,x^5}{5}-\frac {117\,x^4}{4}-86\,x^3+2\,x^2+24\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 42, normalized size = 0.93 \begin {gather*} - 135 x^{8} - \frac {1188 x^{7}}{7} + 111 x^{6} + \frac {949 x^{5}}{5} - \frac {117 x^{4}}{4} - 86 x^{3} + 2 x^{2} + 24 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________