Optimal. Leaf size=6 \[ \frac {B x}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {21, 8}
\begin {gather*} \frac {B x}{b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 8
Rule 21
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 = 0.00, size = 6, normalized size = 1.00 \begin {gather*} \frac {B x}{b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.05, size = 7, normalized size = 1.17
method | result | size |
default | \(\frac {B x}{b}\) | \(7\) |
risch | \(\frac {B x}{b}\) | \(7\) |
norman | \(\frac {\frac {B x}{b}+\frac {B x \left (\tan ^{2}\left (\frac {x}{2}\right )\right )}{b}}{1+\tan ^{2}\left (\frac {x}{2}\right )}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: ValueError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.32, size = 6, normalized size = 1.00 \begin {gather*} \frac {B x}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.14, size = 3, normalized size = 0.50 \begin {gather*} \frac {B x}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.44, size = 6, normalized size = 1.00 \begin {gather*} \frac {B x}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 7.70, size = 6, normalized size = 1.00 \begin {gather*} \frac {B\,x}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________