Optimal. Leaf size=14 \[ \frac{(c+d x)^4}{4 d} \]
[Out]
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Rubi [A] time = 0.00710458, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{(c+d x)^4}{4 d} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 1.3032, size = 8, normalized size = 0.57 \[ \frac{\left (c + d x\right )^{4}}{4 d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**3,x)
[Out]
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Mathematica [A] time = 0.00203093, size = 14, normalized size = 1. \[ \frac{(c+d x)^4}{4 d} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^3,x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[{\frac{ \left ( dx+c \right ) ^{4}}{4\,d}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^3,x)
[Out]
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Maxima [A] time = 1.34283, size = 42, normalized size = 3. \[ \frac{1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac{3}{2} \, c^{2} d x^{2} + c^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.180621, size = 1, normalized size = 0.07 \[ \frac{1}{4} x^{4} d^{3} + x^{3} d^{2} c + \frac{3}{2} x^{2} d c^{2} + x c^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.077014, size = 32, normalized size = 2.29 \[ c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x+c)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.218597, size = 16, normalized size = 1.14 \[ \frac{{\left (d x + c\right )}^{4}}{4 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^3,x, algorithm="giac")
[Out]