Optimal. Leaf size=44 \[ 72 x+210 x^2+\frac {638 x^3}{3}-\frac {769 x^4}{4}-\frac {3366 x^5}{5}-\frac {1215 x^6}{2}-\frac {1350 x^7}{7} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 44, 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 = {78}
\begin {gather*} -\frac {1350 x^7}{7}-\frac {1215 x^6}{2}-\frac {3366 x^5}{5}-\frac {769 x^4}{4}+\frac {638 x^3}{3}+210 x^2+72 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^3 (3+5 x)^2 \, dx &=\int \left (72+420 x+638 x^2-769 x^3-3366 x^4-3645 x^5-1350 x^6\right ) \, dx\\ &=72 x+210 x^2+\frac {638 x^3}{3}-\frac {769 x^4}{4}-\frac {3366 x^5}{5}-\frac {1215 x^6}{2}-\frac {1350 x^7}{7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 44, normalized size = 1.00 \begin {gather*} 72 x+210 x^2+\frac {638 x^3}{3}-\frac {769 x^4}{4}-\frac {3366 x^5}{5}-\frac {1215 x^6}{2}-\frac {1350 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 35, normalized size = 0.80
method | result | size |
gosper | \(-\frac {x \left (81000 x^{6}+255150 x^{5}+282744 x^{4}+80745 x^{3}-89320 x^{2}-88200 x -30240\right )}{420}\) | \(34\) |
default | \(72 x +210 x^{2}+\frac {638}{3} x^{3}-\frac {769}{4} x^{4}-\frac {3366}{5} x^{5}-\frac {1215}{2} x^{6}-\frac {1350}{7} x^{7}\) | \(35\) |
norman | \(72 x +210 x^{2}+\frac {638}{3} x^{3}-\frac {769}{4} x^{4}-\frac {3366}{5} x^{5}-\frac {1215}{2} x^{6}-\frac {1350}{7} x^{7}\) | \(35\) |
risch | \(72 x +210 x^{2}+\frac {638}{3} x^{3}-\frac {769}{4} x^{4}-\frac {3366}{5} x^{5}-\frac {1215}{2} x^{6}-\frac {1350}{7} x^{7}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 34, normalized size = 0.77 \begin {gather*} -\frac {1350}{7} \, x^{7} - \frac {1215}{2} \, x^{6} - \frac {3366}{5} \, x^{5} - \frac {769}{4} \, x^{4} + \frac {638}{3} \, x^{3} + 210 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.29, size = 34, normalized size = 0.77 \begin {gather*} -\frac {1350}{7} \, x^{7} - \frac {1215}{2} \, x^{6} - \frac {3366}{5} \, x^{5} - \frac {769}{4} \, x^{4} + \frac {638}{3} \, x^{3} + 210 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 41, normalized size = 0.93 \begin {gather*} - \frac {1350 x^{7}}{7} - \frac {1215 x^{6}}{2} - \frac {3366 x^{5}}{5} - \frac {769 x^{4}}{4} + \frac {638 x^{3}}{3} + 210 x^{2} + 72 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.72, size = 34, normalized size = 0.77 \begin {gather*} -\frac {1350}{7} \, x^{7} - \frac {1215}{2} \, x^{6} - \frac {3366}{5} \, x^{5} - \frac {769}{4} \, x^{4} + \frac {638}{3} \, x^{3} + 210 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 34, normalized size = 0.77 \begin {gather*} -\frac {1350\,x^7}{7}-\frac {1215\,x^6}{2}-\frac {3366\,x^5}{5}-\frac {769\,x^4}{4}+\frac {638\,x^3}{3}+210\,x^2+72\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________