Optimal. Leaf size=10 \[ \frac{\log (c+d x)}{d} \]
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Rubi [A] time = 0.0050334, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.074, Rules used = {626, 31} \[ \frac{\log (c+d x)}{d} \]
Antiderivative was successfully verified.
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Rule 626
Rule 31
Rubi steps
\begin{align*} \int \frac{a+b x}{a c+(b c+a d) x+b d x^2} \, dx &=\int \frac{1}{c+d x} \, dx\\ &=\frac{\log (c+d x)}{d}\\ \end{align*}
Mathematica [A] time = 0.0011979, size = 10, normalized size = 1. \[ \frac{\log (c+d x)}{d} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.039, size = 11, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( dx+c \right ) }{d}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04392, size = 14, normalized size = 1.4 \begin{align*} \frac{\log \left (d x + c\right )}{d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40938, size = 22, normalized size = 2.2 \begin{align*} \frac{\log \left (d x + c\right )}{d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.139582, size = 7, normalized size = 0.7 \begin{align*} \frac{\log{\left (c + d x \right )}}{d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18707, size = 15, normalized size = 1.5 \begin{align*} \frac{\log \left ({\left | d x + c \right |}\right )}{d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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