Optimal. Leaf size=17 \[ \frac{1}{2} d \left (a+b x+c x^2\right )^2 \]
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Rubi [A] time = 0.0144629, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{1}{2} d \left (a+b x+c x^2\right )^2 \]
Antiderivative was successfully verified.
[In] Int[(b*d + 2*c*d*x)*(a + b*x + c*x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ d \int ^{a + b x + c x^{2}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*d*x+b*d)*(c*x**2+b*x+a),x)
[Out]
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Mathematica [A] time = 0.00966029, size = 22, normalized size = 1.29 \[ \frac{1}{2} d x (b+c x) (2 a+x (b+c x)) \]
Antiderivative was successfully verified.
[In] Integrate[(b*d + 2*c*d*x)*(a + b*x + c*x^2),x]
[Out]
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Maple [B] time = 0., size = 39, normalized size = 2.3 \[{\frac{{c}^{2}d{x}^{4}}{2}}+bcd{x}^{3}+{\frac{ \left ( 2\,acd+{b}^{2}d \right ){x}^{2}}{2}}+bdax \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*d*x+b*d)*(c*x^2+b*x+a),x)
[Out]
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Maxima [A] time = 0.671946, size = 20, normalized size = 1.18 \[ \frac{1}{2} \,{\left (c x^{2} + b x + a\right )}^{2} d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)*(c*x^2 + b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.190148, size = 1, normalized size = 0.06 \[ \frac{1}{2} x^{4} d c^{2} + x^{3} d c b + \frac{1}{2} x^{2} d b^{2} + x^{2} d c a + x d b a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)*(c*x^2 + b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.094575, size = 39, normalized size = 2.29 \[ a b d x + b c d x^{3} + \frac{c^{2} d x^{4}}{2} + x^{2} \left (a c d + \frac{b^{2} d}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x+b*d)*(c*x**2+b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.212538, size = 51, normalized size = 3. \[ \frac{1}{2} \, c^{2} d x^{4} + b c d x^{3} + \frac{1}{2} \, b^{2} d x^{2} + a c d x^{2} + a b d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*d*x + b*d)*(c*x^2 + b*x + a),x, algorithm="giac")
[Out]