Optimal. Leaf size=23 \[ -\frac{1}{3 b d \left (a+b (c+d x)^3\right )} \]
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Rubi [A] time = 0.0167671, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ -\frac{1}{3 b d \left (a+b (c+d x)^3\right )} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^2/(a + b*(c + d*x)^3)^2,x]
[Out]
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Rubi in Sympy [A] time = 3.98413, size = 17, normalized size = 0.74 \[ - \frac{1}{3 b d \left (a + b \left (c + d x\right )^{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**2/(a+b*(d*x+c)**3)**2,x)
[Out]
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Mathematica [A] time = 0.0236333, size = 23, normalized size = 1. \[ -\frac{1}{3 b d \left (a+b (c+d x)^3\right )} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^2/(a + b*(c + d*x)^3)^2,x]
[Out]
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Maple [B] time = 0.001, size = 44, normalized size = 1.9 \[ -{\frac{1}{3\,bd \left ( b{d}^{3}{x}^{3}+3\,bc{d}^{2}{x}^{2}+3\,b{c}^{2}dx+b{c}^{3}+a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^2/(a+b*(d*x+c)^3)^2,x)
[Out]
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Maxima [A] time = 1.42555, size = 28, normalized size = 1.22 \[ -\frac{1}{3 \,{\left ({\left (d x + c\right )}^{3} b + a\right )} b d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^2/((d*x + c)^3*b + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204081, size = 70, normalized size = 3.04 \[ -\frac{1}{3 \,{\left (b^{2} d^{4} x^{3} + 3 \, b^{2} c d^{3} x^{2} + 3 \, b^{2} c^{2} d^{2} x +{\left (b^{2} c^{3} + a b\right )} d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^2/((d*x + c)^3*b + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.75831, size = 58, normalized size = 2.52 \[ - \frac{1}{3 a b d + 3 b^{2} c^{3} d + 9 b^{2} c^{2} d^{2} x + 9 b^{2} c d^{3} x^{2} + 3 b^{2} d^{4} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x+c)**2/(a+b*(d*x+c)**3)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.215257, size = 28, normalized size = 1.22 \[ -\frac{1}{3 \,{\left ({\left (d x + c\right )}^{3} b + a\right )} b d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^2/((d*x + c)^3*b + a)^2,x, algorithm="giac")
[Out]