Optimal. Leaf size=21 \[ \frac{2}{3} \sin \left (\frac{3 x}{4}\right )-\frac{2}{5} \sin \left (\frac{5 x}{4}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0080012, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {4282} \[ \frac{2}{3} \sin \left (\frac{3 x}{4}\right )-\frac{2}{5} \sin \left (\frac{5 x}{4}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 4282
Rubi steps
\begin{align*} \int \sin \left (\frac{x}{4}\right ) \sin (x) \, dx &=\frac{2}{3} \sin \left (\frac{3 x}{4}\right )-\frac{2}{5} \sin \left (\frac{5 x}{4}\right )\\ \end{align*}
Mathematica [A] time = 0.0108375, size = 21, normalized size = 1. \[ \frac{2}{3} \sin \left (\frac{3 x}{4}\right )-\frac{2}{5} \sin \left (\frac{5 x}{4}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.027, size = 14, normalized size = 0.7 \begin{align*}{\frac{2}{3}\sin \left ({\frac{3\,x}{4}} \right ) }-{\frac{2}{5}\sin \left ({\frac{5\,x}{4}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.924895, size = 18, normalized size = 0.86 \begin{align*} -\frac{2}{5} \, \sin \left (\frac{5}{4} \, x\right ) + \frac{2}{3} \, \sin \left (\frac{3}{4} \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.41178, size = 77, normalized size = 3.67 \begin{align*} -\frac{16}{15} \,{\left (6 \, \cos \left (\frac{1}{4} \, x\right )^{4} - 7 \, \cos \left (\frac{1}{4} \, x\right )^{2} + 1\right )} \sin \left (\frac{1}{4} \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.539427, size = 22, normalized size = 1.05 \begin{align*} - \frac{16 \sin{\left (\frac{x}{4} \right )} \cos{\left (x \right )}}{15} + \frac{4 \sin{\left (x \right )} \cos{\left (\frac{x}{4} \right )}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.04563, size = 18, normalized size = 0.86 \begin{align*} -\frac{2}{5} \, \sin \left (\frac{5}{4} \, x\right ) + \frac{2}{3} \, \sin \left (\frac{3}{4} \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]