Optimal. Leaf size=2 \[ \text {Si}(x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 2, 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 = {3380}
\begin {gather*} \text {Si}(x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 3380
Rubi steps
\begin {align*} \int \frac {\sin (x)}{x} \, dx &=\text {Si}(x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 2, normalized size = 1.00 \begin {gather*} \text {Si}(x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 4 in
optimal.
time = 1.73, size = 2, normalized size = 1.00 \begin {gather*} \text {Si}\left [x\right ] \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 3, normalized size = 1.50
method | result | size |
default | \(\sinIntegral \left (x \right )\) | \(3\) |
meijerg | \(\sinIntegral \left (x \right )\) | \(3\) |
risch | \(-\frac {\pi \,\mathrm {csgn}\left (x \right )}{2}+\sinIntegral \left (x \right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [C] Result contains complex when optimal does not.
time = 0.32, size = 13, normalized size = 6.50 \begin {gather*} -\frac {1}{2} i \, {\rm Ei}\left (i \, x\right ) + \frac {1}{2} i \, {\rm Ei}\left (-i \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.34, size = 2, normalized size = 1.00 \begin {gather*} \operatorname {Si}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.31, size = 2, normalized size = 1.00 \begin {gather*} \operatorname {Si}{\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 2, normalized size = 1.00 \begin {gather*} \mathrm {Si}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.50 \begin {gather*} \mathrm {sinint}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________