Optimal. Leaf size=17 \[ -\frac {1}{2 b c^8 (a+b x)^2} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {21, 32} \begin {gather*} -\frac {1}{2 b c^8 (a+b x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 21
Rule 32
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{(a c+b c x)^8} \, dx &=\frac {\int \frac {1}{(a+b x)^3} \, dx}{c^8}\\ &=-\frac {1}{2 b c^8 (a+b x)^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {1}{2 b c^8 (a+b x)^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^5}{(a c+b c x)^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.36, size = 33, normalized size = 1.94 \begin {gather*} -\frac {1}{2 \, {\left (b^{3} c^{8} x^{2} + 2 \, a b^{2} c^{8} x + a^{2} b c^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 15, normalized size = 0.88 \begin {gather*} -\frac {1}{2 \, {\left (b x + a\right )}^{2} b c^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.94 \begin {gather*} -\frac {1}{2 \left (b x +a \right )^{2} b \,c^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.33, size = 33, normalized size = 1.94 \begin {gather*} -\frac {1}{2 \, {\left (b^{3} c^{8} x^{2} + 2 \, a b^{2} c^{8} x + a^{2} b c^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 35, normalized size = 2.06 \begin {gather*} -\frac {1}{2\,a^2\,b\,c^8+4\,a\,b^2\,c^8\,x+2\,b^3\,c^8\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.26, size = 36, normalized size = 2.12 \begin {gather*} - \frac {1}{2 a^{2} b c^{8} + 4 a b^{2} c^{8} x + 2 b^{3} c^{8} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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