Optimal. Leaf size=10 \[ \frac {\cosh (a+b x)}{b} \]
[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 = {2718}
\begin {gather*} \frac {\cosh (a+b x)}{b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2718
Rubi steps
\begin {align*} \int \sinh (a+b x) \, dx &=\frac {\cosh (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 {\cosh (a) \cosh (b x)}{b}+\frac {\sinh (a) \sinh (b x)}{b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.15, size = 11, normalized size = 1.10
method | result | size |
derivativedivides | \(\frac {\cosh \left (b x +a \right )}{b}\) | \(11\) |
default | \(\frac {\cosh \left (b x +a \right )}{b}\) | \(11\) |
risch | \(\frac {{\mathrm e}^{b x +a}}{2 b}+\frac {{\mathrm e}^{-b x -a}}{2 b}\) | \(27\) |
meijerg | \(\frac {\sinh \left (a \right ) \sinh \left (b x \right )}{b}-\frac {\cosh \left (a \right ) \sqrt {\pi }\, \left (\frac {1}{\sqrt {\pi }}-\frac {\cosh \left (b x \right )}{\sqrt {\pi }}\right )}{b}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 10, normalized size = 1.00 \begin {gather*} \frac {\cosh \left (b x + a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 10, normalized size = 1.00 \begin {gather*} \frac {\cosh \left (b x + a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 12, normalized size = 1.20 \begin {gather*} \begin {cases} \frac {\cosh {\left (a + b x \right )}}{b} & \text {for}\: b \neq 0 \\x \sinh {\left (a \right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 26 vs.
\(2 (10) = 20\).
time = 0.40, size = 26, normalized size = 2.60 \begin {gather*} \frac {e^{\left (b x + a\right )}}{2 \, b} + \frac {e^{\left (-b x - a\right )}}{2 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 10, normalized size = 1.00 \begin {gather*} \frac {\mathrm {cosh}\left (a+b\,x\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________