Optimal. Leaf size=104 \[ \frac {4096 x^{17}}{17}-1920 x^{16}+\frac {102784 x^{15}}{15}-\frac {75504 x^{14}}{7}-\frac {12095 x^{13}}{13}+31128 x^{12}-\frac {331040 x^{11}}{11}-\frac {169584 x^{10}}{5}+\frac {641152 x^9}{9}+36384 x^8-\frac {566912 x^7}{7}-30720 x^6+\frac {538624 x^5}{5}+139776 x^4+\frac {237568 x^3}{3}+24576 x^2+4096 x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 104, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2061} \[ \frac {4096 x^{17}}{17}-1920 x^{16}+\frac {102784 x^{15}}{15}-\frac {75504 x^{14}}{7}-\frac {12095 x^{13}}{13}+31128 x^{12}-\frac {331040 x^{11}}{11}-\frac {169584 x^{10}}{5}+\frac {641152 x^9}{9}+36384 x^8-\frac {566912 x^7}{7}-30720 x^6+\frac {538624 x^5}{5}+139776 x^4+\frac {237568 x^3}{3}+24576 x^2+4096 x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2061
Rubi steps
\begin {align*} \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^4 \, dx &=\int \left (4096+49152 x+237568 x^2+559104 x^3+538624 x^4-184320 x^5-566912 x^6+291072 x^7+641152 x^8-339168 x^9-331040 x^{10}+373536 x^{11}-12095 x^{12}-151008 x^{13}+102784 x^{14}-30720 x^{15}+4096 x^{16}\right ) \, dx\\ &=4096 x+24576 x^2+\frac {237568 x^3}{3}+139776 x^4+\frac {538624 x^5}{5}-30720 x^6-\frac {566912 x^7}{7}+36384 x^8+\frac {641152 x^9}{9}-\frac {169584 x^{10}}{5}-\frac {331040 x^{11}}{11}+31128 x^{12}-\frac {12095 x^{13}}{13}-\frac {75504 x^{14}}{7}+\frac {102784 x^{15}}{15}-1920 x^{16}+\frac {4096 x^{17}}{17}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 104, normalized size = 1.00 \[ \frac {4096 x^{17}}{17}-1920 x^{16}+\frac {102784 x^{15}}{15}-\frac {75504 x^{14}}{7}-\frac {12095 x^{13}}{13}+31128 x^{12}-\frac {331040 x^{11}}{11}-\frac {169584 x^{10}}{5}+\frac {641152 x^9}{9}+36384 x^8-\frac {566912 x^7}{7}-30720 x^6+\frac {538624 x^5}{5}+139776 x^4+\frac {237568 x^3}{3}+24576 x^2+4096 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.37, size = 84, normalized size = 0.81 \[ \frac {4096}{17} x^{17} - 1920 x^{16} + \frac {102784}{15} x^{15} - \frac {75504}{7} x^{14} - \frac {12095}{13} x^{13} + 31128 x^{12} - \frac {331040}{11} x^{11} - \frac {169584}{5} x^{10} + \frac {641152}{9} x^{9} + 36384 x^{8} - \frac {566912}{7} x^{7} - 30720 x^{6} + \frac {538624}{5} x^{5} + 139776 x^{4} + \frac {237568}{3} x^{3} + 24576 x^{2} + 4096 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.36, size = 84, normalized size = 0.81 \[ \frac {4096}{17} \, x^{17} - 1920 \, x^{16} + \frac {102784}{15} \, x^{15} - \frac {75504}{7} \, x^{14} - \frac {12095}{13} \, x^{13} + 31128 \, x^{12} - \frac {331040}{11} \, x^{11} - \frac {169584}{5} \, x^{10} + \frac {641152}{9} \, x^{9} + 36384 \, x^{8} - \frac {566912}{7} \, x^{7} - 30720 \, x^{6} + \frac {538624}{5} \, x^{5} + 139776 \, x^{4} + \frac {237568}{3} \, x^{3} + 24576 \, x^{2} + 4096 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 85, normalized size = 0.82 \[ \frac {4096}{17} x^{17}-1920 x^{16}+\frac {102784}{15} x^{15}-\frac {75504}{7} x^{14}-\frac {12095}{13} x^{13}+31128 x^{12}-\frac {331040}{11} x^{11}-\frac {169584}{5} x^{10}+\frac {641152}{9} x^{9}+36384 x^{8}-\frac {566912}{7} x^{7}-30720 x^{6}+\frac {538624}{5} x^{5}+139776 x^{4}+\frac {237568}{3} x^{3}+24576 x^{2}+4096 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.66, size = 84, normalized size = 0.81 \[ \frac {4096}{17} \, x^{17} - 1920 \, x^{16} + \frac {102784}{15} \, x^{15} - \frac {75504}{7} \, x^{14} - \frac {12095}{13} \, x^{13} + 31128 \, x^{12} - \frac {331040}{11} \, x^{11} - \frac {169584}{5} \, x^{10} + \frac {641152}{9} \, x^{9} + 36384 \, x^{8} - \frac {566912}{7} \, x^{7} - 30720 \, x^{6} + \frac {538624}{5} \, x^{5} + 139776 \, x^{4} + \frac {237568}{3} \, x^{3} + 24576 \, x^{2} + 4096 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.23, size = 84, normalized size = 0.81 \[ \frac {4096\,x^{17}}{17}-1920\,x^{16}+\frac {102784\,x^{15}}{15}-\frac {75504\,x^{14}}{7}-\frac {12095\,x^{13}}{13}+31128\,x^{12}-\frac {331040\,x^{11}}{11}-\frac {169584\,x^{10}}{5}+\frac {641152\,x^9}{9}+36384\,x^8-\frac {566912\,x^7}{7}-30720\,x^6+\frac {538624\,x^5}{5}+139776\,x^4+\frac {237568\,x^3}{3}+24576\,x^2+4096\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 100, normalized size = 0.96 \[ \frac {4096 x^{17}}{17} - 1920 x^{16} + \frac {102784 x^{15}}{15} - \frac {75504 x^{14}}{7} - \frac {12095 x^{13}}{13} + 31128 x^{12} - \frac {331040 x^{11}}{11} - \frac {169584 x^{10}}{5} + \frac {641152 x^{9}}{9} + 36384 x^{8} - \frac {566912 x^{7}}{7} - 30720 x^{6} + \frac {538624 x^{5}}{5} + 139776 x^{4} + \frac {237568 x^{3}}{3} + 24576 x^{2} + 4096 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________