Optimal. Leaf size=55 \[ \frac{1}{4} e x^4 (b e+2 c d)+\frac{1}{3} d x^3 (2 b e+c d)+\frac{1}{2} b d^2 x^2+\frac{1}{5} c e^2 x^5 \]
[Out]
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Rubi [A] time = 0.113674, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{1}{4} e x^4 (b e+2 c d)+\frac{1}{3} d x^3 (2 b e+c d)+\frac{1}{2} b d^2 x^2+\frac{1}{5} c e^2 x^5 \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)^2*(b*x + c*x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ b d^{2} \int x\, dx + \frac{c e^{2} x^{5}}{5} + \frac{d x^{3} \left (2 b e + c d\right )}{3} + \frac{e x^{4} \left (b e + 2 c d\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**2*(c*x**2+b*x),x)
[Out]
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Mathematica [A] time = 0.0190143, size = 49, normalized size = 0.89 \[ \frac{1}{60} x^2 \left (15 e x^2 (b e+2 c d)+20 d x (2 b e+c d)+30 b d^2+12 c e^2 x^3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)^2*(b*x + c*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 52, normalized size = 1. \[{\frac{c{e}^{2}{x}^{5}}{5}}+{\frac{ \left ({e}^{2}b+2\,dec \right ){x}^{4}}{4}}+{\frac{ \left ( 2\,bde+c{d}^{2} \right ){x}^{3}}{3}}+{\frac{b{d}^{2}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^2*(c*x^2+b*x),x)
[Out]
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Maxima [A] time = 0.716565, size = 69, normalized size = 1.25 \[ \frac{1}{5} \, c e^{2} x^{5} + \frac{1}{2} \, b d^{2} x^{2} + \frac{1}{4} \,{\left (2 \, c d e + b e^{2}\right )} x^{4} + \frac{1}{3} \,{\left (c d^{2} + 2 \, b d e\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(e*x + d)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215561, size = 1, normalized size = 0.02 \[ \frac{1}{5} x^{5} e^{2} c + \frac{1}{2} x^{4} e d c + \frac{1}{4} x^{4} e^{2} b + \frac{1}{3} x^{3} d^{2} c + \frac{2}{3} x^{3} e d b + \frac{1}{2} x^{2} d^{2} b \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(e*x + d)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.112424, size = 54, normalized size = 0.98 \[ \frac{b d^{2} x^{2}}{2} + \frac{c e^{2} x^{5}}{5} + x^{4} \left (\frac{b e^{2}}{4} + \frac{c d e}{2}\right ) + x^{3} \left (\frac{2 b d e}{3} + \frac{c d^{2}}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**2*(c*x**2+b*x),x)
[Out]
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GIAC/XCAS [A] time = 0.206213, size = 72, normalized size = 1.31 \[ \frac{1}{5} \, c x^{5} e^{2} + \frac{1}{2} \, c d x^{4} e + \frac{1}{3} \, c d^{2} x^{3} + \frac{1}{4} \, b x^{4} e^{2} + \frac{2}{3} \, b d x^{3} e + \frac{1}{2} \, b d^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(e*x + d)^2,x, algorithm="giac")
[Out]