Optimal. Leaf size=22 \[ \frac{3}{25} \sin (5 x)-\frac{1}{5} (3 x+2) \cos (5 x) \]
[Out]
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Rubi [A] time = 0.0213374, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{3}{25} \sin (5 x)-\frac{1}{5} (3 x+2) \cos (5 x) \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)*Sin[5*x],x]
[Out]
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Rubi in Sympy [A] time = 1.15993, size = 20, normalized size = 0.91 \[ - \left (\frac{3 x}{5} + \frac{2}{5}\right ) \cos{\left (5 x \right )} + \frac{3 \sin{\left (5 x \right )}}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)*sin(5*x),x)
[Out]
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Mathematica [A] time = 0.00817653, size = 26, normalized size = 1.18 \[ \frac{3}{25} \sin (5 x)-\frac{3}{5} x \cos (5 x)-\frac{2}{5} \cos (5 x) \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)*Sin[5*x],x]
[Out]
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Maple [A] time = 0.019, size = 21, normalized size = 1. \[ -{\frac{2\,\cos \left ( 5\,x \right ) }{5}}+{\frac{3\,\sin \left ( 5\,x \right ) }{25}}-{\frac{3\,\cos \left ( 5\,x \right ) x}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)*sin(5*x),x)
[Out]
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Maxima [A] time = 1.3251, size = 27, normalized size = 1.23 \[ -\frac{3}{5} \, x \cos \left (5 \, x\right ) - \frac{2}{5} \, \cos \left (5 \, x\right ) + \frac{3}{25} \, \sin \left (5 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*sin(5*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215428, size = 24, normalized size = 1.09 \[ -\frac{1}{5} \,{\left (3 \, x + 2\right )} \cos \left (5 \, x\right ) + \frac{3}{25} \, \sin \left (5 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*sin(5*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.212422, size = 26, normalized size = 1.18 \[ - \frac{3 x \cos{\left (5 x \right )}}{5} + \frac{3 \sin{\left (5 x \right )}}{25} - \frac{2 \cos{\left (5 x \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)*sin(5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.217808, size = 24, normalized size = 1.09 \[ -\frac{1}{5} \,{\left (3 \, x + 2\right )} \cos \left (5 \, x\right ) + \frac{3}{25} \, \sin \left (5 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)*sin(5*x),x, algorithm="giac")
[Out]