Optimal. Leaf size=18 \[ \frac {x}{b}-\frac {a \log (a+b x)}{b^2} \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {43} \[ \frac {x}{b}-\frac {a \log (a+b x)}{b^2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {x}{a+b x} \, dx &=\int \left (\frac {1}{b}-\frac {a}{b (a+b x)}\right ) \, dx\\ &=\frac {x}{b}-\frac {a \log (a+b x)}{b^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {x}{b}-\frac {a \log (a+b x)}{b^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 17, normalized size = 0.94 \[ \frac {b x - a \log \left (b x + a\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 19, normalized size = 1.06 \[ \frac {x}{b} - \frac {a \log \left ({\left | b x + a \right |}\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 19, normalized size = 1.06 \[ -\frac {a \ln \left (b x +a \right )}{b^{2}}+\frac {x}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 18, normalized size = 1.00 \[ \frac {x}{b} - \frac {a \log \left (b x + a\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 18, normalized size = 1.00 \[ -\frac {a\,\ln \left (a+b\,x\right )-b\,x}{b^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.78 \[ - \frac {a \log {\left (a + b x \right )}}{b^{2}} + \frac {x}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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