Optimal. Leaf size=22 \[ \frac {3 x}{2}+\cos (2 x)-\frac {1}{4} \cos (2 x) \sin (2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2723}
\begin {gather*} \frac {3 x}{2}+\cos (2 x)-\frac {1}{4} \sin (2 x) \cos (2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2723
Rubi steps
\begin {align*} \int (1-\sin (2 x))^2 \, dx &=\frac {3 x}{2}+\cos (2 x)-\frac {1}{4} \cos (2 x) \sin (2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 18, normalized size = 0.82 \begin {gather*} \frac {3 x}{2}+\cos (2 x)-\frac {1}{8} \sin (4 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Mathics [A]
time = 2.02, size = 14, normalized size = 0.64 \begin {gather*} \frac {3 x}{2}+\text {Cos}\left [2 x\right ]-\frac {\text {Sin}\left [4 x\right ]}{8} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.04, size = 19, normalized size = 0.86
method | result | size |
risch | \(\frac {3 x}{2}-\frac {\sin \left (4 x \right )}{8}+\cos \left (2 x \right )\) | \(15\) |
derivativedivides | \(\frac {3 x}{2}+\cos \left (2 x \right )-\frac {\cos \left (2 x \right ) \sin \left (2 x \right )}{4}\) | \(19\) |
default | \(\frac {3 x}{2}+\cos \left (2 x \right )-\frac {\cos \left (2 x \right ) \sin \left (2 x \right )}{4}\) | \(19\) |
norman | \(\frac {2 \left (\tan ^{2}\left (x \right )\right )+\frac {3 x}{2}+\frac {\left (\tan ^{3}\left (x \right )\right )}{2}+3 x \left (\tan ^{2}\left (x \right )\right )+\frac {3 x \left (\tan ^{4}\left (x \right )\right )}{2}-\frac {\tan \left (x \right )}{2}+2}{\left (1+\tan ^{2}\left (x \right )\right )^{2}}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 14, normalized size = 0.64 \begin {gather*} \frac {3}{2} \, x + \cos \left (2 \, x\right ) - \frac {1}{8} \, \sin \left (4 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 18, normalized size = 0.82 \begin {gather*} -\frac {1}{4} \, \cos \left (2 \, x\right ) \sin \left (2 \, x\right ) + \frac {3}{2} \, x + \cos \left (2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 37, normalized size = 1.68 \begin {gather*} \frac {x \sin ^{2}{\left (2 x \right )}}{2} + \frac {x \cos ^{2}{\left (2 x \right )}}{2} + x - \frac {\sin {\left (2 x \right )} \cos {\left (2 x \right )}}{4} + \cos {\left (2 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 28, normalized size = 1.27 \begin {gather*} \frac {x}{2}-\frac {\sin \left (4 x\right )}{8}+\frac {\cos \left (2 x\right )}{2}+\frac {\cos \left (2 x\right )}{2}+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.26, size = 14, normalized size = 0.64 \begin {gather*} \frac {3\,x}{2}+\cos \left (2\,x\right )-\frac {\sin \left (4\,x\right )}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________