Optimal. Leaf size=32 \[ \frac {9 x^5}{5}-4 x^6+\frac {22 x^7}{7}-x^8+\frac {x^9}{9} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {712}
\begin {gather*} \frac {x^9}{9}-x^8+\frac {22 x^7}{7}-4 x^6+\frac {9 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 712
Rubi steps
\begin {align*} \int x^4 \left (3-4 x+x^2\right )^2 \, dx &=\int \left (9 x^4-24 x^5+22 x^6-8 x^7+x^8\right ) \, dx\\ &=\frac {9 x^5}{5}-4 x^6+\frac {22 x^7}{7}-x^8+\frac {x^9}{9}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 32, normalized size = 1.00 \begin {gather*} \frac {9 x^5}{5}-4 x^6+\frac {22 x^7}{7}-x^8+\frac {x^9}{9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.73, size = 27, normalized size = 0.84
method | result | size |
gosper | \(\frac {x^{5} \left (35 x^{4}-315 x^{3}+990 x^{2}-1260 x +567\right )}{315}\) | \(26\) |
default | \(\frac {9}{5} x^{5}-4 x^{6}+\frac {22}{7} x^{7}-x^{8}+\frac {1}{9} x^{9}\) | \(27\) |
norman | \(\frac {9}{5} x^{5}-4 x^{6}+\frac {22}{7} x^{7}-x^{8}+\frac {1}{9} x^{9}\) | \(27\) |
risch | \(\frac {9}{5} x^{5}-4 x^{6}+\frac {22}{7} x^{7}-x^{8}+\frac {1}{9} x^{9}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 26, normalized size = 0.81 \begin {gather*} \frac {1}{9} \, x^{9} - x^{8} + \frac {22}{7} \, x^{7} - 4 \, x^{6} + \frac {9}{5} \, x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 3.79, size = 26, normalized size = 0.81 \begin {gather*} \frac {1}{9} \, x^{9} - x^{8} + \frac {22}{7} \, x^{7} - 4 \, x^{6} + \frac {9}{5} \, x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 26, normalized size = 0.81 \begin {gather*} \frac {x^{9}}{9} - x^{8} + \frac {22 x^{7}}{7} - 4 x^{6} + \frac {9 x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.99, size = 26, normalized size = 0.81 \begin {gather*} \frac {1}{9} \, x^{9} - x^{8} + \frac {22}{7} \, x^{7} - 4 \, x^{6} + \frac {9}{5} \, x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 26, normalized size = 0.81 \begin {gather*} \frac {x^9}{9}-x^8+\frac {22\,x^7}{7}-4\,x^6+\frac {9\,x^5}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________