Optimal. Leaf size=19 \[ -\frac {\left (a+b x^2\right )^7}{14 a x^{14}} \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {28, 264} \begin {gather*} -\frac {\left (a+b x^2\right )^7}{14 a x^{14}} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a^2+2 a b x^2+b^2 x^4\right )^3}{x^{15}} \, dx &=\frac {\int \frac {\left (a b+b^2 x^2\right )^6}{x^{15}} \, dx}{b^6}\\ &=-\frac {\left (a+b x^2\right )^7}{14 a x^{14}}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 82, normalized size = 4.32 \begin {gather*} -\frac {a^6}{14 x^{14}}-\frac {a^5 b}{2 x^{12}}-\frac {3 a^4 b^2}{2 x^{10}}-\frac {5 a^3 b^3}{2 x^8}-\frac {5 a^2 b^4}{2 x^6}-\frac {3 a b^5}{2 x^4}-\frac {b^6}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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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^{15}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.81, size = 68, normalized size = 3.58 \begin {gather*} -\frac {7 \, b^{6} x^{12} + 21 \, a b^{5} x^{10} + 35 \, a^{2} b^{4} x^{8} + 35 \, a^{3} b^{3} x^{6} + 21 \, a^{4} b^{2} x^{4} + 7 \, a^{5} b x^{2} + a^{6}}{14 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 68, normalized size = 3.58 \begin {gather*} -\frac {7 \, b^{6} x^{12} + 21 \, a b^{5} x^{10} + 35 \, a^{2} b^{4} x^{8} + 35 \, a^{3} b^{3} x^{6} + 21 \, a^{4} b^{2} x^{4} + 7 \, a^{5} b x^{2} + a^{6}}{14 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 69, normalized size = 3.63 \begin {gather*} -\frac {b^{6}}{2 x^{2}}-\frac {3 a \,b^{5}}{2 x^{4}}-\frac {5 a^{2} b^{4}}{2 x^{6}}-\frac {5 a^{3} b^{3}}{2 x^{8}}-\frac {3 a^{4} b^{2}}{2 x^{10}}-\frac {a^{5} b}{2 x^{12}}-\frac {a^{6}}{14 x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.38, size = 68, normalized size = 3.58 \begin {gather*} -\frac {7 \, b^{6} x^{12} + 21 \, a b^{5} x^{10} + 35 \, a^{2} b^{4} x^{8} + 35 \, a^{3} b^{3} x^{6} + 21 \, a^{4} b^{2} x^{4} + 7 \, a^{5} b x^{2} + a^{6}}{14 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.36, size = 70, normalized size = 3.68 \begin {gather*} -\frac {\frac {a^6}{14}+\frac {a^5\,b\,x^2}{2}+\frac {3\,a^4\,b^2\,x^4}{2}+\frac {5\,a^3\,b^3\,x^6}{2}+\frac {5\,a^2\,b^4\,x^8}{2}+\frac {3\,a\,b^5\,x^{10}}{2}+\frac {b^6\,x^{12}}{2}}{x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.63, size = 73, normalized size = 3.84 \begin {gather*} \frac {- a^{6} - 7 a^{5} b x^{2} - 21 a^{4} b^{2} x^{4} - 35 a^{3} b^{3} x^{6} - 35 a^{2} b^{4} x^{8} - 21 a b^{5} x^{10} - 7 b^{6} x^{12}}{14 x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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