Optimal. Leaf size=39 \[ \frac{1}{4} (d+e x)^4 \left (a-\frac{c d^2}{e^2}\right )+\frac{c d (d+e x)^5}{5 e^2} \]
[Out]
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Rubi [A] time = 0.065713, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 33, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.061 \[ \frac{1}{4} (d+e x)^4 \left (a-\frac{c d^2}{e^2}\right )+\frac{c d (d+e x)^5}{5 e^2} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]
[Out]
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Rubi in Sympy [A] time = 21.8165, size = 36, normalized size = 0.92 \[ \frac{c d \left (d + e x\right )^{5}}{5 e^{2}} + \frac{\left (d + e x\right )^{4} \left (a e^{2} - c d^{2}\right )}{4 e^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)
[Out]
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Mathematica [A] time = 0.0383957, size = 73, normalized size = 1.87 \[ \frac{1}{20} x \left (5 a e \left (4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right )+c d x \left (10 d^3+20 d^2 e x+15 d e^2 x^2+4 e^3 x^3\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2),x]
[Out]
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Maple [B] time = 0.001, size = 112, normalized size = 2.9 \[{\frac{d{e}^{3}c{x}^{5}}{5}}+{\frac{ \left ( 2\,{d}^{2}{e}^{2}c+{e}^{2} \left ( a{e}^{2}+c{d}^{2} \right ) \right ){x}^{4}}{4}}+{\frac{ \left ( c{d}^{3}e+2\,de \left ( a{e}^{2}+c{d}^{2} \right ) +ad{e}^{3} \right ){x}^{3}}{3}}+{\frac{ \left ({d}^{2} \left ( a{e}^{2}+c{d}^{2} \right ) +2\,a{d}^{2}{e}^{2} \right ){x}^{2}}{2}}+{d}^{3}aex \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^2*(a*e*d+(a*e^2+c*d^2)*x+c*d*e*x^2),x)
[Out]
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Maxima [A] time = 0.718356, size = 101, normalized size = 2.59 \[ \frac{1}{5} \, c d e^{3} x^{5} + a d^{3} e x + \frac{1}{4} \,{\left (3 \, c d^{2} e^{2} + a e^{4}\right )} x^{4} +{\left (c d^{3} e + a d e^{3}\right )} x^{3} + \frac{1}{2} \,{\left (c d^{4} + 3 \, a d^{2} e^{2}\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(e*x + d)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.178018, size = 1, normalized size = 0.03 \[ \frac{1}{5} x^{5} e^{3} d c + \frac{3}{4} x^{4} e^{2} d^{2} c + \frac{1}{4} x^{4} e^{4} a + x^{3} e d^{3} c + x^{3} e^{3} d a + \frac{1}{2} x^{2} d^{4} c + \frac{3}{2} x^{2} e^{2} d^{2} a + x e d^{3} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(e*x + d)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.138646, size = 80, normalized size = 2.05 \[ a d^{3} e x + \frac{c d e^{3} x^{5}}{5} + x^{4} \left (\frac{a e^{4}}{4} + \frac{3 c d^{2} e^{2}}{4}\right ) + x^{3} \left (a d e^{3} + c d^{3} e\right ) + x^{2} \left (\frac{3 a d^{2} e^{2}}{2} + \frac{c d^{4}}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.208626, size = 101, normalized size = 2.59 \[ \frac{1}{5} \, c d x^{5} e^{3} + \frac{3}{4} \, c d^{2} x^{4} e^{2} + c d^{3} x^{3} e + \frac{1}{2} \, c d^{4} x^{2} + \frac{1}{4} \, a x^{4} e^{4} + a d x^{3} e^{3} + \frac{3}{2} \, a d^{2} x^{2} e^{2} + a d^{3} x e \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(e*x + d)^2,x, algorithm="giac")
[Out]