Optimal. Leaf size=10 \[ \frac {\sin (a+b x)}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2637} \[ \frac {\sin (a+b x)}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2637
Rubi steps
\begin {align*} \int \cos (a+b x) \, dx &=\frac {\sin (a+b x)}{b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.01, size = 21, normalized size = 2.10 \[ \frac {\sin (a) \cos (b x)}{b}+\frac {\cos (a) \sin (b x)}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 10, normalized size = 1.00 \[ \frac {\sin \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.92, size = 10, normalized size = 1.00 \[ \frac {\sin \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 11, normalized size = 1.10 \[ \frac {\sin \left (b x +a \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.41, size = 10, normalized size = 1.00 \[ \frac {\sin \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 10, normalized size = 1.00 \[ \frac {\sin \left (a+b\,x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 12, normalized size = 1.20 \[ \begin {cases} \frac {\sin {\left (a + b x \right )}}{b} & \text {for}\: b \neq 0 \\x \cos {\relax (a )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________