Optimal. Leaf size=10 \[ \frac {1}{4} \sin ^2\left (x^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 10, 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 = {3441} \[ \frac {1}{4} \sin ^2\left (x^2\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3441
Rubi steps
\begin {align*} \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx &=\frac {1}{4} \sin ^2\left (x^2\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ -\frac {1}{4} \cos ^2\left (x^2\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 8, normalized size = 0.80 \[ -\frac {1}{4} \, \cos \left (x^{2}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.01, size = 8, normalized size = 0.80 \[ -\frac {1}{4} \, \cos \left (x^{2}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 9, normalized size = 0.90 \[ -\frac {\left (\cos ^{2}\left (x^{2}\right )\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.53, size = 8, normalized size = 0.80 \[ -\frac {1}{4} \, \cos \left (x^{2}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 8, normalized size = 0.80 \[ \frac {{\sin \left (x^2\right )}^2}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.33, size = 8, normalized size = 0.80 \[ - \frac {\cos ^{2}{\left (x^{2} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________