Optimal. Leaf size=4 \[ \sin (\sin (\sin (x))) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {4419, 2717}
\begin {gather*} \sin (\sin (\sin (x))) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2717
Rule 4419
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\text {Subst}(\int \cos (x) \cos (\sin (x)) \, dx,x,\sin (x))\\ &=\text {Subst}(\int \cos (x) \, dx,x,\sin (\sin (x)))\\ &=\sin (\sin (\sin (x)))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 3.40, size = 4, normalized size = 1.00 \begin {gather*} \sin (\sin (\sin (x))) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 9.08, size = 5, normalized size = 1.25
method | result | size |
derivativedivides | \(\sin \left (\sin \left (\sin \left (x \right )\right )\right )\) | \(5\) |
default | \(\sin \left (\sin \left (\sin \left (x \right )\right )\right )\) | \(5\) |
risch | \(\sin \left (\sin \left (\sin \left (x \right )\right )\right )\) | \(5\) |
parallelrisch | \(\sin \left (\sin \left (\sin \left (x \right )\right )\right )\) | \(5\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.33, size = 4, normalized size = 1.00 \begin {gather*} \sin \left (\sin \left (\sin \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 41 vs.
\(2 (4) = 8\).
time = 0.61, size = 41, normalized size = 10.25 \begin {gather*} \sin \left (\frac {2 \, \tan \left (\frac {\tan \left (\frac {1}{2} \, x\right )}{\tan \left (\frac {1}{2} \, x\right )^{2} + 1}\right )}{\tan \left (\frac {\tan \left (\frac {1}{2} \, x\right )}{\tan \left (\frac {1}{2} \, x\right )^{2} + 1}\right )^{2} + 1}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 1.13, size = 5, normalized size = 1.25 \begin {gather*} \sin {\left (\sin {\left (\sin {\left (x \right )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.50, size = 4, normalized size = 1.00 \begin {gather*} \sin \left (\sin \left (\sin \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.11, size = 4, normalized size = 1.00 \begin {gather*} \sin \left (\sin \left (\sin \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________