Optimal. Leaf size=10 \[ \frac{\log (A+B x)}{B} \]
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Rubi [A] time = 0.0023645, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {27, 31} \[ \frac{\log (A+B x)}{B} \]
Antiderivative was successfully verified.
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Rule 27
Rule 31
Rubi steps
\begin{align*} \int \frac{A+B x}{A^2+2 A B x+B^2 x^2} \, dx &=\int \frac{1}{A+B x} \, dx\\ &=\frac{\log (A+B x)}{B}\\ \end{align*}
Mathematica [A] time = 0.0010704, size = 10, normalized size = 1. \[ \frac{\log (A+B x)}{B} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 11, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( Bx+A \right ) }{B}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.03434, size = 30, normalized size = 3. \begin{align*} \frac{\log \left (B^{2} x^{2} + 2 \, A B x + A^{2}\right )}{2 \, B} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.74428, size = 22, normalized size = 2.2 \begin{align*} \frac{\log \left (B x + A\right )}{B} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.183329, size = 7, normalized size = 0.7 \begin{align*} \frac{\log{\left (A + B x \right )}}{B} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22143, size = 15, normalized size = 1.5 \begin{align*} \frac{\log \left ({\left | B x + A \right |}\right )}{B} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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