Optimal. Leaf size=19 \[ \frac {(a+b x) \log (a+b x)}{b}-x \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2389, 2295} \[ \frac {(a+b x) \log (a+b x)}{b}-x \]
Antiderivative was successfully verified.
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Rule 2295
Rule 2389
Rubi steps
\begin {align*} \int \log (a+b x) \, dx &=\frac {\operatorname {Subst}(\int \log (x) \, dx,x,a+b x)}{b}\\ &=-x+\frac {(a+b x) \log (a+b x)}{b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \frac {(a+b x) \log (a+b x)}{b}-x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 22, normalized size = 1.16 \[ -\frac {b x - {\left (b x + a\right )} \log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 23, normalized size = 1.21 \[ -\frac {b x - {\left (b x + a\right )} \log \left (b x + a\right ) + a}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 30, normalized size = 1.58 \[ x \ln \left (b x +a \right )+\frac {a \ln \left (b x +a \right )}{b}-x -\frac {a}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 23, normalized size = 1.21 \[ -\frac {b x - {\left (b x + a\right )} \log \left (b x + a\right ) + a}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 23, normalized size = 1.21 \[ x\,\ln \left (a+b\,x\right )-x+\frac {a\,\ln \left (a+b\,x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 24, normalized size = 1.26 \[ - b \left (- \frac {a \log {\left (a + b x \right )}}{b^{2}} + \frac {x}{b}\right ) + x \log {\left (a + b x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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