Optimal. Leaf size=8 \[ \log (x (b+c x)) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0056778, antiderivative size = 9, normalized size of antiderivative = 1.12, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {72} \[ \log (b+c x)+\log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 72
Rubi steps
\begin{align*} \int \frac{b+2 c x}{x (b+c x)} \, dx &=\int \left (\frac{1}{x}+\frac{c}{b+c x}\right ) \, dx\\ &=\log (x)+\log (b+c x)\\ \end{align*}
Mathematica [A] time = 0.0047065, size = 9, normalized size = 1.12 \[ \log (b+c x)+\log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 9, normalized size = 1.1 \begin{align*} \ln \left ( x \left ( cx+b \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.924054, size = 12, normalized size = 1.5 \begin{align*} \log \left (c x + b\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.940105, size = 24, normalized size = 3. \begin{align*} \log \left (c x^{2} + b x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.27032, size = 8, normalized size = 1. \begin{align*} \log{\left (b x + c x^{2} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06982, size = 15, normalized size = 1.88 \begin{align*} \log \left ({\left | c x + b \right |}\right ) + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]