Optimal. Leaf size=14 \[ \frac{\log \left (\sqrt{a}+x\right )}{\sqrt{a}} \]
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Rubi [A] time = 0.0021261, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {31} \[ \frac{\log \left (\sqrt{a}+x\right )}{\sqrt{a}} \]
Antiderivative was successfully verified.
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Rule 31
Rubi steps
\begin{align*} \int \frac{1}{a+\sqrt{a} x} \, dx &=\frac{\log \left (\sqrt{a}+x\right )}{\sqrt{a}}\\ \end{align*}
Mathematica [A] time = 0.0039626, size = 16, normalized size = 1.14 \[ \frac{\log \left (\sqrt{a} x+a\right )}{\sqrt{a}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \begin{align*}{\ln \left ( a+x\sqrt{a} \right ){\frac{1}{\sqrt{a}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08035, size = 16, normalized size = 1.14 \begin{align*} \frac{\log \left (\sqrt{a} x + a\right )}{\sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.60401, size = 35, normalized size = 2.5 \begin{align*} \frac{\log \left (x + \sqrt{a}\right )}{\sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.068242, size = 14, normalized size = 1. \begin{align*} \frac{\log{\left (\sqrt{a} x + a \right )}}{\sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20454, size = 18, normalized size = 1.29 \begin{align*} \frac{\log \left ({\left | \sqrt{a} x + a \right |}\right )}{\sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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