Optimal. Leaf size=79 \[ \frac {a^6 x^7}{7}+\frac {2}{3} a^5 b x^9+\frac {15}{11} a^4 b^2 x^{11}+\frac {20}{13} a^3 b^3 x^{13}+a^2 b^4 x^{15}+\frac {6}{17} a b^5 x^{17}+\frac {b^6 x^{19}}{19} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 79, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {28, 270} \[ a^2 b^4 x^{15}+\frac {20}{13} a^3 b^3 x^{13}+\frac {15}{11} a^4 b^2 x^{11}+\frac {2}{3} a^5 b x^9+\frac {a^6 x^7}{7}+\frac {6}{17} a b^5 x^{17}+\frac {b^6 x^{19}}{19} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 270
Rubi steps
\begin {align*} \int x^6 \left (a^2+2 a b x^2+b^2 x^4\right )^3 \, dx &=\frac {\int x^6 \left (a b+b^2 x^2\right )^6 \, dx}{b^6}\\ &=\frac {\int \left (a^6 b^6 x^6+6 a^5 b^7 x^8+15 a^4 b^8 x^{10}+20 a^3 b^9 x^{12}+15 a^2 b^{10} x^{14}+6 a b^{11} x^{16}+b^{12} x^{18}\right ) \, dx}{b^6}\\ &=\frac {a^6 x^7}{7}+\frac {2}{3} a^5 b x^9+\frac {15}{11} a^4 b^2 x^{11}+\frac {20}{13} a^3 b^3 x^{13}+a^2 b^4 x^{15}+\frac {6}{17} a b^5 x^{17}+\frac {b^6 x^{19}}{19}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 79, normalized size = 1.00 \[ \frac {a^6 x^7}{7}+\frac {2}{3} a^5 b x^9+\frac {15}{11} a^4 b^2 x^{11}+\frac {20}{13} a^3 b^3 x^{13}+a^2 b^4 x^{15}+\frac {6}{17} a b^5 x^{17}+\frac {b^6 x^{19}}{19} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 67, normalized size = 0.85 \[ \frac {1}{19} x^{19} b^{6} + \frac {6}{17} x^{17} b^{5} a + x^{15} b^{4} a^{2} + \frac {20}{13} x^{13} b^{3} a^{3} + \frac {15}{11} x^{11} b^{2} a^{4} + \frac {2}{3} x^{9} b a^{5} + \frac {1}{7} x^{7} a^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 67, normalized size = 0.85 \[ \frac {1}{19} \, b^{6} x^{19} + \frac {6}{17} \, a b^{5} x^{17} + a^{2} b^{4} x^{15} + \frac {20}{13} \, a^{3} b^{3} x^{13} + \frac {15}{11} \, a^{4} b^{2} x^{11} + \frac {2}{3} \, a^{5} b x^{9} + \frac {1}{7} \, a^{6} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 68, normalized size = 0.86 \[ \frac {1}{19} b^{6} x^{19}+\frac {6}{17} a \,b^{5} x^{17}+a^{2} b^{4} x^{15}+\frac {20}{13} a^{3} b^{3} x^{13}+\frac {15}{11} a^{4} b^{2} x^{11}+\frac {2}{3} a^{5} b \,x^{9}+\frac {1}{7} a^{6} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.39, size = 67, normalized size = 0.85 \[ \frac {1}{19} \, b^{6} x^{19} + \frac {6}{17} \, a b^{5} x^{17} + a^{2} b^{4} x^{15} + \frac {20}{13} \, a^{3} b^{3} x^{13} + \frac {15}{11} \, a^{4} b^{2} x^{11} + \frac {2}{3} \, a^{5} b x^{9} + \frac {1}{7} \, a^{6} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 67, normalized size = 0.85 \[ \frac {a^6\,x^7}{7}+\frac {2\,a^5\,b\,x^9}{3}+\frac {15\,a^4\,b^2\,x^{11}}{11}+\frac {20\,a^3\,b^3\,x^{13}}{13}+a^2\,b^4\,x^{15}+\frac {6\,a\,b^5\,x^{17}}{17}+\frac {b^6\,x^{19}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 76, normalized size = 0.96 \[ \frac {a^{6} x^{7}}{7} + \frac {2 a^{5} b x^{9}}{3} + \frac {15 a^{4} b^{2} x^{11}}{11} + \frac {20 a^{3} b^{3} x^{13}}{13} + a^{2} b^{4} x^{15} + \frac {6 a b^{5} x^{17}}{17} + \frac {b^{6} x^{19}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________