Optimal. Leaf size=34 \[ -\frac {25}{48} (1-2 x)^6+\frac {11}{4} (1-2 x)^5-\frac {121}{32} (1-2 x)^4 \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \begin {gather*} -\frac {25}{48} (1-2 x)^6+\frac {11}{4} (1-2 x)^5-\frac {121}{32} (1-2 x)^4 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int (1-2 x)^3 (3+5 x)^2 \, dx &=\int \left (\frac {121}{4} (1-2 x)^3-\frac {55}{2} (1-2 x)^4+\frac {25}{4} (1-2 x)^5\right ) \, dx\\ &=-\frac {121}{32} (1-2 x)^4+\frac {11}{4} (1-2 x)^5-\frac {25}{48} (1-2 x)^6\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 35, normalized size = 1.03 \begin {gather*} -\frac {100 x^6}{3}+12 x^5+\frac {69 x^4}{2}-\frac {47 x^3}{3}-12 x^2+9 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 (3+5 x)^2 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.08, size = 29, normalized size = 0.85 \begin {gather*} -\frac {100}{3} x^{6} + 12 x^{5} + \frac {69}{2} x^{4} - \frac {47}{3} x^{3} - 12 x^{2} + 9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.92, size = 29, normalized size = 0.85 \begin {gather*} -\frac {100}{3} \, x^{6} + 12 \, x^{5} + \frac {69}{2} \, x^{4} - \frac {47}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 30, normalized size = 0.88 \begin {gather*} -\frac {100}{3} x^{6}+12 x^{5}+\frac {69}{2} x^{4}-\frac {47}{3} x^{3}-12 x^{2}+9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.60, size = 29, normalized size = 0.85 \begin {gather*} -\frac {100}{3} \, x^{6} + 12 \, x^{5} + \frac {69}{2} \, x^{4} - \frac {47}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 29, normalized size = 0.85 \begin {gather*} -\frac {100\,x^6}{3}+12\,x^5+\frac {69\,x^4}{2}-\frac {47\,x^3}{3}-12\,x^2+9\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 32, normalized size = 0.94 \begin {gather*} - \frac {100 x^{6}}{3} + 12 x^{5} + \frac {69 x^{4}}{2} - \frac {47 x^{3}}{3} - 12 x^{2} + 9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________