Optimal. Leaf size=18 \[ \frac{1}{16} \sin (4 x)-\frac{1}{4} x \cos (4 x) \]
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Rubi [A] time = 0.0096751, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {3296, 2637} \[ \frac{1}{16} \sin (4 x)-\frac{1}{4} x \cos (4 x) \]
Antiderivative was successfully verified.
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Rule 3296
Rule 2637
Rubi steps
\begin{align*} \int x \sin (4 x) \, dx &=-\frac{1}{4} x \cos (4 x)+\frac{1}{4} \int \cos (4 x) \, dx\\ &=-\frac{1}{4} x \cos (4 x)+\frac{1}{16} \sin (4 x)\\ \end{align*}
Mathematica [A] time = 0.010573, size = 18, normalized size = 1. \[ \frac{1}{16} \sin (4 x)-\frac{1}{4} x \cos (4 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 15, normalized size = 0.8 \begin{align*} -{\frac{x\cos \left ( 4\,x \right ) }{4}}+{\frac{\sin \left ( 4\,x \right ) }{16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.948765, size = 19, normalized size = 1.06 \begin{align*} -\frac{1}{4} \, x \cos \left (4 \, x\right ) + \frac{1}{16} \, \sin \left (4 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.94667, size = 45, normalized size = 2.5 \begin{align*} -\frac{1}{4} \, x \cos \left (4 \, x\right ) + \frac{1}{16} \, \sin \left (4 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.167363, size = 14, normalized size = 0.78 \begin{align*} - \frac{x \cos{\left (4 x \right )}}{4} + \frac{\sin{\left (4 x \right )}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0504, size = 19, normalized size = 1.06 \begin{align*} -\frac{1}{4} \, x \cos \left (4 \, x\right ) + \frac{1}{16} \, \sin \left (4 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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