Optimal. Leaf size=43 \[ -\frac {a^3}{14 x^{14}}-\frac {a^2 b}{4 x^{12}}-\frac {3 a b^2}{10 x^{10}}-\frac {b^3}{8 x^8} \]
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Rubi [A] time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac {a^2 b}{4 x^{12}}-\frac {a^3}{14 x^{14}}-\frac {3 a b^2}{10 x^{10}}-\frac {b^3}{8 x^8} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^3}{x^{15}} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x^8} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {a^3}{x^8}+\frac {3 a^2 b}{x^7}+\frac {3 a b^2}{x^6}+\frac {b^3}{x^5}\right ) \, dx,x,x^2\right )\\ &=-\frac {a^3}{14 x^{14}}-\frac {a^2 b}{4 x^{12}}-\frac {3 a b^2}{10 x^{10}}-\frac {b^3}{8 x^8}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 43, normalized size = 1.00 \[ -\frac {a^3}{14 x^{14}}-\frac {a^2 b}{4 x^{12}}-\frac {3 a b^2}{10 x^{10}}-\frac {b^3}{8 x^8} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 37, normalized size = 0.86 \[ -\frac {35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 37, normalized size = 0.86 \[ -\frac {35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.84 \[ -\frac {b^{3}}{8 x^{8}}-\frac {3 a \,b^{2}}{10 x^{10}}-\frac {a^{2} b}{4 x^{12}}-\frac {a^{3}}{14 x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 37, normalized size = 0.86 \[ -\frac {35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.86 \[ -\frac {\frac {a^3}{14}+\frac {a^2\,b\,x^2}{4}+\frac {3\,a\,b^2\,x^4}{10}+\frac {b^3\,x^6}{8}}{x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 39, normalized size = 0.91 \[ \frac {- 20 a^{3} - 70 a^{2} b x^{2} - 84 a b^{2} x^{4} - 35 b^{3} x^{6}}{280 x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
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