Optimal. Leaf size=15 \[ \frac {\log ^2(a+b x)}{2 b} \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2437, 2338}
\begin {gather*} \frac {\log ^2(a+b x)}{2 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 2338
Rule 2437
Rubi steps
\begin {align*} \int \frac {\log (a+b x)}{a+b x} \, dx &=\frac {\text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b}\\ &=\frac {\log ^2(a+b x)}{2 b}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {\log ^2(a+b x)}{2 b} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 14, normalized size = 0.93
method | result | size |
derivativedivides | \(\frac {\ln \left (b x +a \right )^{2}}{2 b}\) | \(14\) |
default | \(\frac {\ln \left (b x +a \right )^{2}}{2 b}\) | \(14\) |
norman | \(\frac {\ln \left (b x +a \right )^{2}}{2 b}\) | \(14\) |
risch | \(\frac {\ln \left (b x +a \right )^{2}}{2 b}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.87 \begin {gather*} \frac {\log \left (b x + a\right )^{2}}{2 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 13, normalized size = 0.87 \begin {gather*} \frac {\log \left (b x + a\right )^{2}}{2 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 10, normalized size = 0.67 \begin {gather*} \frac {\log {\left (a + b x \right )}^{2}}{2 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.49, size = 13, normalized size = 0.87 \begin {gather*} \frac {\log \left (b x + a\right )^{2}}{2 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.55, size = 13, normalized size = 0.87 \begin {gather*} \frac {{\ln \left (a+b\,x\right )}^2}{2\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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