Optimal. Leaf size=43 \[ -\frac {a^3}{18 x^{18}}-\frac {a^2 b}{5 x^{15}}-\frac {a b^2}{4 x^{12}}-\frac {b^3}{9 x^9} \]
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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} \[ -\frac {a^2 b}{5 x^{15}}-\frac {a^3}{18 x^{18}}-\frac {a b^2}{4 x^{12}}-\frac {b^3}{9 x^9} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x^{19}} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x^7} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (\frac {a^3}{x^7}+\frac {3 a^2 b}{x^6}+\frac {3 a b^2}{x^5}+\frac {b^3}{x^4}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^3}{18 x^{18}}-\frac {a^2 b}{5 x^{15}}-\frac {a b^2}{4 x^{12}}-\frac {b^3}{9 x^9}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \[ -\frac {a^3}{18 x^{18}}-\frac {a^2 b}{5 x^{15}}-\frac {a b^2}{4 x^{12}}-\frac {b^3}{9 x^9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 37, normalized size = 0.86 \[ -\frac {20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 37, normalized size = 0.86 \[ -\frac {20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.84 \[ -\frac {b^{3}}{9 x^{9}}-\frac {a \,b^{2}}{4 x^{12}}-\frac {a^{2} b}{5 x^{15}}-\frac {a^{3}}{18 x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 37, normalized size = 0.86 \[ -\frac {20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]
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 \[ -\frac {\frac {a^3}{18}+\frac {a^2\,b\,x^3}{5}+\frac {a\,b^2\,x^6}{4}+\frac {b^3\,x^9}{9}}{x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.57, size = 39, normalized size = 0.91 \[ \frac {- 10 a^{3} - 36 a^{2} b x^{3} - 45 a b^{2} x^{6} - 20 b^{3} x^{9}}{180 x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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