Optimal. Leaf size=54 \[ \frac {a^2 x^6}{6}+\frac {1}{8} x^8 \left (2 a c+b^2\right )+\frac {2}{7} a b x^7+\frac {2}{9} b c x^9+\frac {c^2 x^{10}}{10} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1585, 698} \[ \frac {a^2 x^6}{6}+\frac {1}{8} x^8 \left (2 a c+b^2\right )+\frac {2}{7} a b x^7+\frac {2}{9} b c x^9+\frac {c^2 x^{10}}{10} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 698
Rule 1585
Rubi steps
\begin {align*} \int x \left (a x^2+b x^3+c x^4\right )^2 \, dx &=\int x^5 \left (a+b x+c x^2\right )^2 \, dx\\ &=\int \left (a^2 x^5+2 a b x^6+\left (b^2+2 a c\right ) x^7+2 b c x^8+c^2 x^9\right ) \, dx\\ &=\frac {a^2 x^6}{6}+\frac {2}{7} a b x^7+\frac {1}{8} \left (b^2+2 a c\right ) x^8+\frac {2}{9} b c x^9+\frac {c^2 x^{10}}{10}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 54, normalized size = 1.00 \[ \frac {a^2 x^6}{6}+\frac {1}{8} x^8 \left (2 a c+b^2\right )+\frac {2}{7} a b x^7+\frac {2}{9} b c x^9+\frac {c^2 x^{10}}{10} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.59, size = 46, normalized size = 0.85 \[ \frac {1}{10} x^{10} c^{2} + \frac {2}{9} x^{9} c b + \frac {1}{8} x^{8} b^{2} + \frac {1}{4} x^{8} c a + \frac {2}{7} x^{7} b a + \frac {1}{6} x^{6} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.48, size = 46, normalized size = 0.85 \[ \frac {1}{10} \, c^{2} x^{10} + \frac {2}{9} \, b c x^{9} + \frac {1}{8} \, b^{2} x^{8} + \frac {1}{4} \, a c x^{8} + \frac {2}{7} \, a b x^{7} + \frac {1}{6} \, a^{2} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 45, normalized size = 0.83 \[ \frac {c^{2} x^{10}}{10}+\frac {2 b c \,x^{9}}{9}+\frac {2 a b \,x^{7}}{7}+\frac {a^{2} x^{6}}{6}+\frac {\left (2 a c +b^{2}\right ) x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.44, size = 44, normalized size = 0.81 \[ \frac {1}{10} \, c^{2} x^{10} + \frac {2}{9} \, b c x^{9} + \frac {2}{7} \, a b x^{7} + \frac {1}{8} \, {\left (b^{2} + 2 \, a c\right )} x^{8} + \frac {1}{6} \, a^{2} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 45, normalized size = 0.83 \[ x^8\,\left (\frac {b^2}{8}+\frac {a\,c}{4}\right )+\frac {a^2\,x^6}{6}+\frac {c^2\,x^{10}}{10}+\frac {2\,a\,b\,x^7}{7}+\frac {2\,b\,c\,x^9}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 49, normalized size = 0.91 \[ \frac {a^{2} x^{6}}{6} + \frac {2 a b x^{7}}{7} + \frac {2 b c x^{9}}{9} + \frac {c^{2} x^{10}}{10} + x^{8} \left (\frac {a c}{4} + \frac {b^{2}}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________