Optimal. Leaf size=82 \[ -\frac {a^6}{21 x^{21}}-\frac {6 a^5 b}{19 x^{19}}-\frac {15 a^4 b^2}{17 x^{17}}-\frac {4 a^3 b^3}{3 x^{15}}-\frac {15 a^2 b^4}{13 x^{13}}-\frac {6 a b^5}{11 x^{11}}-\frac {b^6}{9 x^9} \]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 82, 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} \begin {gather*} -\frac {15 a^4 b^2}{17 x^{17}}-\frac {4 a^3 b^3}{3 x^{15}}-\frac {15 a^2 b^4}{13 x^{13}}-\frac {6 a^5 b}{19 x^{19}}-\frac {a^6}{21 x^{21}}-\frac {6 a b^5}{11 x^{11}}-\frac {b^6}{9 x^9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a^2+2 a b x^2+b^2 x^4\right )^3}{x^{22}} \, dx &=\frac {\int \frac {\left (a b+b^2 x^2\right )^6}{x^{22}} \, dx}{b^6}\\ &=\frac {\int \left (\frac {a^6 b^6}{x^{22}}+\frac {6 a^5 b^7}{x^{20}}+\frac {15 a^4 b^8}{x^{18}}+\frac {20 a^3 b^9}{x^{16}}+\frac {15 a^2 b^{10}}{x^{14}}+\frac {6 a b^{11}}{x^{12}}+\frac {b^{12}}{x^{10}}\right ) \, dx}{b^6}\\ &=-\frac {a^6}{21 x^{21}}-\frac {6 a^5 b}{19 x^{19}}-\frac {15 a^4 b^2}{17 x^{17}}-\frac {4 a^3 b^3}{3 x^{15}}-\frac {15 a^2 b^4}{13 x^{13}}-\frac {6 a b^5}{11 x^{11}}-\frac {b^6}{9 x^9}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 82, normalized size = 1.00 \begin {gather*} -\frac {a^6}{21 x^{21}}-\frac {6 a^5 b}{19 x^{19}}-\frac {15 a^4 b^2}{17 x^{17}}-\frac {4 a^3 b^3}{3 x^{15}}-\frac {15 a^2 b^4}{13 x^{13}}-\frac {6 a b^5}{11 x^{11}}-\frac {b^6}{9 x^9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a^2+2 a b x^2+b^2 x^4\right )^3}{x^{22}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.85, size = 70, normalized size = 0.85 \begin {gather*} -\frac {323323 \, b^{6} x^{12} + 1587222 \, a b^{5} x^{10} + 3357585 \, a^{2} b^{4} x^{8} + 3879876 \, a^{3} b^{3} x^{6} + 2567565 \, a^{4} b^{2} x^{4} + 918918 \, a^{5} b x^{2} + 138567 \, a^{6}}{2909907 \, x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 70, normalized size = 0.85 \begin {gather*} -\frac {323323 \, b^{6} x^{12} + 1587222 \, a b^{5} x^{10} + 3357585 \, a^{2} b^{4} x^{8} + 3879876 \, a^{3} b^{3} x^{6} + 2567565 \, a^{4} b^{2} x^{4} + 918918 \, a^{5} b x^{2} + 138567 \, a^{6}}{2909907 \, x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 69, normalized size = 0.84 \begin {gather*} -\frac {b^{6}}{9 x^{9}}-\frac {6 a \,b^{5}}{11 x^{11}}-\frac {15 a^{2} b^{4}}{13 x^{13}}-\frac {4 a^{3} b^{3}}{3 x^{15}}-\frac {15 a^{4} b^{2}}{17 x^{17}}-\frac {6 a^{5} b}{19 x^{19}}-\frac {a^{6}}{21 x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.34, size = 70, normalized size = 0.85 \begin {gather*} -\frac {323323 \, b^{6} x^{12} + 1587222 \, a b^{5} x^{10} + 3357585 \, a^{2} b^{4} x^{8} + 3879876 \, a^{3} b^{3} x^{6} + 2567565 \, a^{4} b^{2} x^{4} + 918918 \, a^{5} b x^{2} + 138567 \, a^{6}}{2909907 \, x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 70, normalized size = 0.85 \begin {gather*} -\frac {\frac {a^6}{21}+\frac {6\,a^5\,b\,x^2}{19}+\frac {15\,a^4\,b^2\,x^4}{17}+\frac {4\,a^3\,b^3\,x^6}{3}+\frac {15\,a^2\,b^4\,x^8}{13}+\frac {6\,a\,b^5\,x^{10}}{11}+\frac {b^6\,x^{12}}{9}}{x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.76, size = 75, normalized size = 0.91 \begin {gather*} \frac {- 138567 a^{6} - 918918 a^{5} b x^{2} - 2567565 a^{4} b^{2} x^{4} - 3879876 a^{3} b^{3} x^{6} - 3357585 a^{2} b^{4} x^{8} - 1587222 a b^{5} x^{10} - 323323 b^{6} x^{12}}{2909907 x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________