Optimal. Leaf size=14 \[ -\frac {1}{2 b (a+b x)^2} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \[ -\frac {1}{2 b (a+b x)^2} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{(a+b x)^3} \, dx &=-\frac {1}{2 b (a+b x)^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ -\frac {1}{2 b (a+b x)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 24, normalized size = 1.71 \[ -\frac {1}{2 \, {\left (b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.95, size = 12, normalized size = 0.86 \[ -\frac {1}{2 \, {\left (b x + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.93 \[ -\frac {1}{2 \left (b x +a \right )^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 12, normalized size = 0.86 \[ -\frac {1}{2 \, {\left (b x + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 26, normalized size = 1.86 \[ -\frac {1}{2\,a^2\,b+4\,a\,b^2\,x+2\,b^3\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.21, size = 26, normalized size = 1.86 \[ - \frac {1}{2 a^{2} b + 4 a b^{2} x + 2 b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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