Optimal. Leaf size=18 \[ \frac{x}{b}-\frac{a \log (a+b x)}{b^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0099383, antiderivative size = 18, normalized size of antiderivative = 1., 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.
[In]
[Out]
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*}
Mathematica [A] time = 0.0023684, size = 18, normalized size = 1. \[ \frac{x}{b}-\frac{a \log (a+b x)}{b^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 19, normalized size = 1.1 \begin{align*}{\frac{x}{b}}-{\frac{a\ln \left ( bx+a \right ) }{{b}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.950947, size = 24, normalized size = 1.33 \begin{align*} \frac{x}{b} - \frac{a \log \left (b x + a\right )}{b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.88243, size = 38, normalized size = 2.11 \begin{align*} \frac{b x - a \log \left (b x + a\right )}{b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.260511, size = 14, normalized size = 0.78 \begin{align*} - \frac{a \log{\left (a + b x \right )}}{b^{2}} + \frac{x}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.08058, size = 26, normalized size = 1.44 \begin{align*} \frac{x}{b} - \frac{a \log \left ({\left | b x + a \right |}\right )}{b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]