Optimal. Leaf size=14 \[ -\frac {1}{5 b (a+b x)^5} \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {2058, 32} \[ -\frac {1}{5 b (a+b x)^5} \]
Antiderivative was successfully verified.
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Rule 32
Rule 2058
Rubi steps
\begin {align*} \int \frac {1}{\left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^2} \, dx &=\int \frac {1}{(a+b x)^6} \, dx\\ &=-\frac {1}{5 b (a+b x)^5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ -\frac {1}{5 b (a+b x)^5} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.73, size = 57, normalized size = 4.07 \[ -\frac {1}{5 \, {\left (b^{6} x^{5} + 5 \, a b^{5} x^{4} + 10 \, a^{2} b^{4} x^{3} + 10 \, a^{3} b^{3} x^{2} + 5 \, a^{4} b^{2} x + a^{5} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 12, normalized size = 0.86 \[ -\frac {1}{5 \, {\left (b x + a\right )}^{5} b} \]
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 \[ -\frac {1}{5 \left (b x +a \right )^{5} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.71, size = 57, normalized size = 4.07 \[ -\frac {1}{5 \, {\left (b^{6} x^{5} + 5 \, a b^{5} x^{4} + 10 \, a^{2} b^{4} x^{3} + 10 \, a^{3} b^{3} x^{2} + 5 \, a^{4} b^{2} x + a^{5} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.05, size = 59, normalized size = 4.21 \[ -\frac {1}{5\,a^5\,b+25\,a^4\,b^2\,x+50\,a^3\,b^3\,x^2+50\,a^2\,b^4\,x^3+25\,a\,b^5\,x^4+5\,b^6\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.35, size = 61, normalized size = 4.36 \[ - \frac {1}{5 a^{5} b + 25 a^{4} b^{2} x + 50 a^{3} b^{3} x^{2} + 50 a^{2} b^{4} x^{3} + 25 a b^{5} x^{4} + 5 b^{6} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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