Optimal. Leaf size=13 \[ \frac {\log (a+b x)}{b c^6} \]
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Rubi [A] time = 0.00, antiderivative size = 13, 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, 31} \begin {gather*} \frac {\log (a+b x)}{b c^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 21
Rule 31
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{(a c+b c x)^6} \, dx &=\frac {\int \frac {1}{a+b x} \, dx}{c^6}\\ &=\frac {\log (a+b x)}{b c^6}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {\log (a+b x)}{b c^6} \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)^6} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.33, size = 13, normalized size = 1.00 \begin {gather*} \frac {\log \left (b x + a\right )}{b c^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.95, size = 14, normalized size = 1.08 \begin {gather*} \frac {\log \left ({\left | b x + a \right |}\right )}{b c^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 1.08 \begin {gather*} \frac {\ln \left (b x +a \right )}{b \,c^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 13, normalized size = 1.00 \begin {gather*} \frac {\log \left (b x + a\right )}{b c^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 13, normalized size = 1.00 \begin {gather*} \frac {\ln \left (a+b\,x\right )}{b\,c^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 17, normalized size = 1.31 \begin {gather*} \frac {\log {\left (a c^{6} + b c^{6} x \right )}}{b c^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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