Optimal. Leaf size=43 \[ -\frac {a^3}{7 x^7}-\frac {a^2 b}{2 x^6}-\frac {3 a b^2}{5 x^5}-\frac {b^3}{4 x^4} \]
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Rubi [A] time = 0.01, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ -\frac {a^2 b}{2 x^6}-\frac {a^3}{7 x^7}-\frac {3 a b^2}{5 x^5}-\frac {b^3}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{x^8} \, dx &=\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\\ &=-\frac {a^3}{7 x^7}-\frac {a^2 b}{2 x^6}-\frac {3 a b^2}{5 x^5}-\frac {b^3}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \[ -\frac {a^3}{7 x^7}-\frac {a^2 b}{2 x^6}-\frac {3 a b^2}{5 x^5}-\frac {b^3}{4 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 35, normalized size = 0.81 \[ -\frac {35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.12, size = 35, normalized size = 0.81 \[ -\frac {35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \]
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 \[ -\frac {b^{3}}{4 x^{4}}-\frac {3 a \,b^{2}}{5 x^{5}}-\frac {a^{2} b}{2 x^{6}}-\frac {a^{3}}{7 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 35, normalized size = 0.81 \[ -\frac {35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 35, normalized size = 0.81 \[ -\frac {\frac {a^3}{7}+\frac {a^2\,b\,x}{2}+\frac {3\,a\,b^2\,x^2}{5}+\frac {b^3\,x^3}{4}}{x^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 37, normalized size = 0.86 \[ \frac {- 20 a^{3} - 70 a^{2} b x - 84 a b^{2} x^{2} - 35 b^{3} x^{3}}{140 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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