Integrand size = 10, antiderivative size = 10 \[ \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx=\frac {1}{4} \sin ^2\left (x^2\right ) \]
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Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {3522} \[ \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx=\frac {1}{4} \sin ^2\left (x^2\right ) \]
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Rule 3522
Rubi steps \begin{align*} \text {integral}& = \frac {1}{4} \sin ^2\left (x^2\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx=-\frac {1}{4} \cos ^2\left (x^2\right ) \]
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Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90
method | result | size |
derivativedivides | \(-\frac {\left (\cos ^{2}\left (x^{2}\right )\right )}{4}\) | \(9\) |
default | \(-\frac {\left (\cos ^{2}\left (x^{2}\right )\right )}{4}\) | \(9\) |
risch | \(-\frac {\cos \left (2 x^{2}\right )}{8}\) | \(9\) |
parallelrisch | \(-\frac {\cos \left (2 x^{2}\right )}{8}+\frac {1}{8}\) | \(11\) |
meijerg | \(\frac {\sqrt {\pi }\, \left (\frac {1}{\sqrt {\pi }}-\frac {\cos \left (2 x^{2}\right )}{\sqrt {\pi }}\right )}{8}\) | \(21\) |
norman | \(\frac {\tan ^{2}\left (\frac {x^{2}}{2}\right )}{\left (1+\tan ^{2}\left (\frac {x^{2}}{2}\right )\right )^{2}}\) | \(22\) |
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none
Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx=-\frac {1}{4} \, \cos \left (x^{2}\right )^{2} \]
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Time = 0.10 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx=- \frac {\cos ^{2}{\left (x^{2} \right )}}{4} \]
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none
Time = 0.17 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx=-\frac {1}{4} \, \cos \left (x^{2}\right )^{2} \]
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none
Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx=-\frac {1}{4} \, \cos \left (x^{2}\right )^{2} \]
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Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx=\frac {{\sin \left (x^2\right )}^2}{4} \]
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