Optimal. Leaf size=96 \[ 432 x+1080 x^2+2856 x^3+5144 x^4+\frac {43083 x^5}{5}+\frac {64529 x^6}{6}+\frac {91349 x^7}{7}+\frac {94881 x^8}{8}+\frac {103583 x^9}{9}+\frac {75311 x^{10}}{10}+\frac {68583 x^{11}}{11}+\frac {30395 x^{12}}{12}+\frac {27050 x^{13}}{13}+\frac {2250 x^{14}}{7}+\frac {1000 x^{15}}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.04, antiderivative size = 96, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {1671}
\begin {gather*} \frac {1000 x^{15}}{3}+\frac {2250 x^{14}}{7}+\frac {27050 x^{13}}{13}+\frac {30395 x^{12}}{12}+\frac {68583 x^{11}}{11}+\frac {75311 x^{10}}{10}+\frac {103583 x^9}{9}+\frac {94881 x^8}{8}+\frac {91349 x^7}{7}+\frac {64529 x^6}{6}+\frac {43083 x^5}{5}+5144 x^4+2856 x^3+1080 x^2+432 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1671
Rubi steps
\begin {align*} \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right )^4 \, dx &=\int \left (432+2160 x+8568 x^2+20576 x^3+43083 x^4+64529 x^5+91349 x^6+94881 x^7+103583 x^8+75311 x^9+68583 x^{10}+30395 x^{11}+27050 x^{12}+4500 x^{13}+5000 x^{14}\right ) \, dx\\ &=432 x+1080 x^2+2856 x^3+5144 x^4+\frac {43083 x^5}{5}+\frac {64529 x^6}{6}+\frac {91349 x^7}{7}+\frac {94881 x^8}{8}+\frac {103583 x^9}{9}+\frac {75311 x^{10}}{10}+\frac {68583 x^{11}}{11}+\frac {30395 x^{12}}{12}+\frac {27050 x^{13}}{13}+\frac {2250 x^{14}}{7}+\frac {1000 x^{15}}{3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 96, normalized size = 1.00 \begin {gather*} 432 x+1080 x^2+2856 x^3+5144 x^4+\frac {43083 x^5}{5}+\frac {64529 x^6}{6}+\frac {91349 x^7}{7}+\frac {94881 x^8}{8}+\frac {103583 x^9}{9}+\frac {75311 x^{10}}{10}+\frac {68583 x^{11}}{11}+\frac {30395 x^{12}}{12}+\frac {27050 x^{13}}{13}+\frac {2250 x^{14}}{7}+\frac {1000 x^{15}}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 75, normalized size = 0.78
method | result | size |
gosper | \(432 x +1080 x^{2}+2856 x^{3}+5144 x^{4}+\frac {43083}{5} x^{5}+\frac {64529}{6} x^{6}+\frac {91349}{7} x^{7}+\frac {94881}{8} x^{8}+\frac {103583}{9} x^{9}+\frac {75311}{10} x^{10}+\frac {68583}{11} x^{11}+\frac {30395}{12} x^{12}+\frac {27050}{13} x^{13}+\frac {2250}{7} x^{14}+\frac {1000}{3} x^{15}\) | \(75\) |
default | \(432 x +1080 x^{2}+2856 x^{3}+5144 x^{4}+\frac {43083}{5} x^{5}+\frac {64529}{6} x^{6}+\frac {91349}{7} x^{7}+\frac {94881}{8} x^{8}+\frac {103583}{9} x^{9}+\frac {75311}{10} x^{10}+\frac {68583}{11} x^{11}+\frac {30395}{12} x^{12}+\frac {27050}{13} x^{13}+\frac {2250}{7} x^{14}+\frac {1000}{3} x^{15}\) | \(75\) |
norman | \(432 x +1080 x^{2}+2856 x^{3}+5144 x^{4}+\frac {43083}{5} x^{5}+\frac {64529}{6} x^{6}+\frac {91349}{7} x^{7}+\frac {94881}{8} x^{8}+\frac {103583}{9} x^{9}+\frac {75311}{10} x^{10}+\frac {68583}{11} x^{11}+\frac {30395}{12} x^{12}+\frac {27050}{13} x^{13}+\frac {2250}{7} x^{14}+\frac {1000}{3} x^{15}\) | \(75\) |
risch | \(432 x +1080 x^{2}+2856 x^{3}+5144 x^{4}+\frac {43083}{5} x^{5}+\frac {64529}{6} x^{6}+\frac {91349}{7} x^{7}+\frac {94881}{8} x^{8}+\frac {103583}{9} x^{9}+\frac {75311}{10} x^{10}+\frac {68583}{11} x^{11}+\frac {30395}{12} x^{12}+\frac {27050}{13} x^{13}+\frac {2250}{7} x^{14}+\frac {1000}{3} x^{15}\) | \(75\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 74, normalized size = 0.77 \begin {gather*} \frac {1000}{3} \, x^{15} + \frac {2250}{7} \, x^{14} + \frac {27050}{13} \, x^{13} + \frac {30395}{12} \, x^{12} + \frac {68583}{11} \, x^{11} + \frac {75311}{10} \, x^{10} + \frac {103583}{9} \, x^{9} + \frac {94881}{8} \, x^{8} + \frac {91349}{7} \, x^{7} + \frac {64529}{6} \, x^{6} + \frac {43083}{5} \, x^{5} + 5144 \, x^{4} + 2856 \, x^{3} + 1080 \, x^{2} + 432 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 2.05, size = 74, normalized size = 0.77 \begin {gather*} \frac {1000}{3} \, x^{15} + \frac {2250}{7} \, x^{14} + \frac {27050}{13} \, x^{13} + \frac {30395}{12} \, x^{12} + \frac {68583}{11} \, x^{11} + \frac {75311}{10} \, x^{10} + \frac {103583}{9} \, x^{9} + \frac {94881}{8} \, x^{8} + \frac {91349}{7} \, x^{7} + \frac {64529}{6} \, x^{6} + \frac {43083}{5} \, x^{5} + 5144 \, x^{4} + 2856 \, x^{3} + 1080 \, x^{2} + 432 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 92, normalized size = 0.96 \begin {gather*} \frac {1000 x^{15}}{3} + \frac {2250 x^{14}}{7} + \frac {27050 x^{13}}{13} + \frac {30395 x^{12}}{12} + \frac {68583 x^{11}}{11} + \frac {75311 x^{10}}{10} + \frac {103583 x^{9}}{9} + \frac {94881 x^{8}}{8} + \frac {91349 x^{7}}{7} + \frac {64529 x^{6}}{6} + \frac {43083 x^{5}}{5} + 5144 x^{4} + 2856 x^{3} + 1080 x^{2} + 432 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 3.76, size = 74, normalized size = 0.77 \begin {gather*} \frac {1000}{3} \, x^{15} + \frac {2250}{7} \, x^{14} + \frac {27050}{13} \, x^{13} + \frac {30395}{12} \, x^{12} + \frac {68583}{11} \, x^{11} + \frac {75311}{10} \, x^{10} + \frac {103583}{9} \, x^{9} + \frac {94881}{8} \, x^{8} + \frac {91349}{7} \, x^{7} + \frac {64529}{6} \, x^{6} + \frac {43083}{5} \, x^{5} + 5144 \, x^{4} + 2856 \, x^{3} + 1080 \, x^{2} + 432 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.12, size = 74, normalized size = 0.77 \begin {gather*} \frac {1000\,x^{15}}{3}+\frac {2250\,x^{14}}{7}+\frac {27050\,x^{13}}{13}+\frac {30395\,x^{12}}{12}+\frac {68583\,x^{11}}{11}+\frac {75311\,x^{10}}{10}+\frac {103583\,x^9}{9}+\frac {94881\,x^8}{8}+\frac {91349\,x^7}{7}+\frac {64529\,x^6}{6}+\frac {43083\,x^5}{5}+5144\,x^4+2856\,x^3+1080\,x^2+432\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________