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 = {2717}
\begin {gather*} \frac {\sin (a+b x)}{b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2717
Rubi steps
\begin {align*} \int \cos (a+b x) \, dx &=\frac {\sin (a+b x)}{b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(21\) vs. \(2(10)=20\).
time = 0.01, size = 21, normalized size = 2.10 \begin {gather*} \frac {\cos (b x) \sin (a)}{b}+\frac {\cos (a) \sin (b x)}{b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 3 in
optimal.
time = 1.73, size = 20, normalized size = 2.00 \begin {gather*} \text {Piecewise}\left [\left \{\left \{\frac {\text {Sin}\left [a+b x\right ]}{b},b\text {!=}0\right \}\right \},x \text {Cos}\left [a\right ]\right ] \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 11, normalized size = 1.10
method | result | size |
derivativedivides | \(\frac {\sin \left (b x +a \right )}{b}\) | \(11\) |
default | \(\frac {\sin \left (b x +a \right )}{b}\) | \(11\) |
risch | \(\frac {\sin \left (b x +a \right )}{b}\) | \(11\) |
norman | \(\frac {2 \tan \left (\frac {b x}{2}+\frac {a}{2}\right )}{b \left (1+\tan ^{2}\left (\frac {b x}{2}+\frac {a}{2}\right )\right )}\) | \(30\) |
meijerg | \(\frac {\cos \left (a \right ) \sin \left (b x \right )}{b}-\frac {\sin \left (a \right ) \sqrt {\pi }\, \left (\frac {1}{\sqrt {\pi }}-\frac {\cos \left (b x \right )}{\sqrt {\pi }}\right )}{b}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.25, size = 10, normalized size = 1.00 \begin {gather*} \frac {\sin \left (b x + a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.31, size = 10, normalized size = 1.00 \begin {gather*} \frac {\sin \left (b x + a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 12, normalized size = 1.20 \begin {gather*} \begin {cases} \frac {\sin {\left (a + b x \right )}}{b} & \text {for}\: b \neq 0 \\x \cos {\left (a \right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 9, normalized size = 0.90 \begin {gather*} \frac {\sin \left (b x+a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 10, normalized size = 1.00 \begin {gather*} \frac {\sin \left (a+b\,x\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________