Optimal. Leaf size=38 \[ \frac{(a+b x)^3 (b d-a e)}{3 b^2}+\frac{e (a+b x)^4}{4 b^2} \]
[Out]
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Rubi [A] time = 0.0779613, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{(a+b x)^3 (b d-a e)}{3 b^2}+\frac{e (a+b x)^4}{4 b^2} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2),x]
[Out]
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Rubi in Sympy [A] time = 17.238, size = 31, normalized size = 0.82 \[ \frac{e \left (a + b x\right )^{4}}{4 b^{2}} - \frac{\left (a + b x\right )^{3} \left (a e - b d\right )}{3 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(b**2*x**2+2*a*b*x+a**2),x)
[Out]
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Mathematica [A] time = 0.0172308, size = 46, normalized size = 1.21 \[ \frac{1}{12} x \left (6 a^2 (2 d+e x)+4 a b x (3 d+2 e x)+b^2 x^2 (4 d+3 e x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2),x]
[Out]
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Maple [A] time = 0.001, size = 49, normalized size = 1.3 \[{\frac{{b}^{2}e{x}^{4}}{4}}+{\frac{ \left ( 2\,bea+{b}^{2}d \right ){x}^{3}}{3}}+{\frac{ \left ( e{a}^{2}+2\,bda \right ){x}^{2}}{2}}+{a}^{2}dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(b^2*x^2+2*a*b*x+a^2),x)
[Out]
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Maxima [A] time = 0.680064, size = 65, normalized size = 1.71 \[ \frac{1}{4} \, b^{2} e x^{4} + a^{2} d x + \frac{1}{3} \,{\left (b^{2} d + 2 \, a b e\right )} x^{3} + \frac{1}{2} \,{\left (2 \, a b d + a^{2} e\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(e*x + d),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.17767, size = 1, normalized size = 0.03 \[ \frac{1}{4} x^{4} e b^{2} + \frac{1}{3} x^{3} d b^{2} + \frac{2}{3} x^{3} e b a + x^{2} d b a + \frac{1}{2} x^{2} e a^{2} + x d a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(e*x + d),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.10759, size = 49, normalized size = 1.29 \[ a^{2} d x + \frac{b^{2} e x^{4}}{4} + x^{3} \left (\frac{2 a b e}{3} + \frac{b^{2} d}{3}\right ) + x^{2} \left (\frac{a^{2} e}{2} + a b d\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(b**2*x**2+2*a*b*x+a**2),x)
[Out]
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GIAC/XCAS [A] time = 0.21, size = 70, normalized size = 1.84 \[ \frac{1}{4} \, b^{2} x^{4} e + \frac{1}{3} \, b^{2} d x^{3} + \frac{2}{3} \, a b x^{3} e + a b d x^{2} + \frac{1}{2} \, a^{2} x^{2} e + a^{2} d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(e*x + d),x, algorithm="giac")
[Out]