Optimal. Leaf size=19 \[ -\frac{\left (a+b x^2\right )^7}{14 a x^{14}} \]
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Rubi [A] time = 0.0066284, antiderivative size = 19, normalized size of antiderivative = 1., 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} \[ -\frac{\left (a+b x^2\right )^7}{14 a x^{14}} \]
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*}
Mathematica [B] time = 0.007406, size = 82, normalized size = 4.32 \[ -\frac{3 a^4 b^2}{2 x^{10}}-\frac{5 a^3 b^3}{2 x^8}-\frac{5 a^2 b^4}{2 x^6}-\frac{a^5 b}{2 x^{12}}-\frac{a^6}{14 x^{14}}-\frac{3 a b^5}{2 x^4}-\frac{b^6}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.048, size = 69, normalized size = 3.6 \begin{align*} -{\frac{{a}^{5}b}{2\,{x}^{12}}}-{\frac{3\,{a}^{4}{b}^{2}}{2\,{x}^{10}}}-{\frac{3\,a{b}^{5}}{2\,{x}^{4}}}-{\frac{{a}^{6}}{14\,{x}^{14}}}-{\frac{{b}^{6}}{2\,{x}^{2}}}-{\frac{5\,{a}^{3}{b}^{3}}{2\,{x}^{8}}}-{\frac{5\,{a}^{2}{b}^{4}}{2\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.9972, size = 92, normalized size = 4.84 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.68576, size = 151, normalized size = 7.95 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.757519, size = 73, normalized size = 3.84 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.17481, size = 92, normalized size = 4.84 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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