Optimal. Leaf size=14 \[ -\frac {1}{4 b (a+b x)^4} \]
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Rubi [A] time = 0.02, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {2058, 32} \[ -\frac {1}{4 b (a+b x)^4} \]
Antiderivative was successfully verified.
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Rule 32
Rule 2058
Rubi steps
\begin {align*} \int \frac {1}{a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5} \, dx &=\int \frac {1}{(a+b x)^5} \, dx\\ &=-\frac {1}{4 b (a+b x)^4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ -\frac {1}{4 b (a+b x)^4} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.83, size = 46, normalized size = 3.29 \[ -\frac {1}{4 \, {\left (b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 12, normalized size = 0.86 \[ -\frac {1}{4 \, {\left (b x + a\right )}^{4} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 0.93 \[ -\frac {1}{4 \left (b x +a \right )^{4} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.69, size = 46, normalized size = 3.29 \[ -\frac {1}{4 \, {\left (b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 48, normalized size = 3.43 \[ -\frac {1}{4\,a^4\,b+16\,a^3\,b^2\,x+24\,a^2\,b^3\,x^2+16\,a\,b^4\,x^3+4\,b^5\,x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.29, size = 49, normalized size = 3.50 \[ - \frac {1}{4 a^{4} b + 16 a^{3} b^{2} x + 24 a^{2} b^{3} x^{2} + 16 a b^{4} x^{3} + 4 b^{5} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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