Optimal. Leaf size=6 \[ \frac{B x}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0013596, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {21, 8} \[ \frac{B x}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 21
Rule 8
Rubi steps
\begin{align*} \int \frac{\frac{a B}{b}+B \sin (x)}{a+b \sin (x)} \, dx &=\frac{B \int 1 \, dx}{b}\\ &=\frac{B x}{b}\\ \end{align*}
Mathematica [A] time = 0.0004145, size = 6, normalized size = 1. \[ \frac{B x}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 7, normalized size = 1.2 \begin{align*}{\frac{Bx}{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.11702, size = 9, normalized size = 1.5 \begin{align*} \frac{B x}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.332326, size = 3, normalized size = 0.5 \begin{align*} \frac{B x}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.28898, size = 8, normalized size = 1.33 \begin{align*} \frac{B x}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]