Optimal. Leaf size=20 \[ \frac{(c+d) (a+b x)^2}{2 b e} \]
[Out]
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Rubi [A] time = 0.0133103, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{(c+d) (a+b x)^2}{2 b e} \]
Antiderivative was successfully verified.
[In] Int[((c + d)*(a + b*x))/e,x]
[Out]
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Rubi in Sympy [A] time = 2.32039, size = 14, normalized size = 0.7 \[ \frac{\left (a + b x\right )^{2} \left (c + d\right )}{2 b e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c+d)*(b*x+a)/e,x)
[Out]
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Mathematica [A] time = 0.00134553, size = 19, normalized size = 0.95 \[ \frac{(c+d) \left (a x+\frac{b x^2}{2}\right )}{e} \]
Antiderivative was successfully verified.
[In] Integrate[((c + d)*(a + b*x))/e,x]
[Out]
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Maple [A] time = 0.002, size = 18, normalized size = 0.9 \[{\frac{c+d}{e} \left ( ax+{\frac{b{x}^{2}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c+d)*(b*x+a)/e,x)
[Out]
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Maxima [A] time = 1.34811, size = 24, normalized size = 1.2 \[ \frac{{\left (b x^{2} + 2 \, a x\right )}{\left (c + d\right )}}{2 \, e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(c + d)/e,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.196058, size = 36, normalized size = 1.8 \[ \frac{{\left (b c + b d\right )} x^{2} + 2 \,{\left (a c + a d\right )} x}{2 \, e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(c + d)/e,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.080573, size = 22, normalized size = 1.1 \[ \frac{x^{2} \left (b c + b d\right )}{2 e} + \frac{x \left (a c + a d\right )}{e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c+d)*(b*x+a)/e,x)
[Out]
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GIAC/XCAS [A] time = 0.223422, size = 23, normalized size = 1.15 \[ \frac{1}{2} \,{\left (b x^{2} + 2 \, a x\right )}{\left (c + d\right )} e^{\left (-1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(c + d)/e,x, algorithm="giac")
[Out]