Optimal. Leaf size=18 \[ \frac{(c+d x)^{n+1}}{d (n+1)} \]
[Out]
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Rubi [A] time = 0.0108916, antiderivative size = 18, 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 \[ \frac{(c+d x)^{n+1}}{d (n+1)} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^n,x]
[Out]
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Rubi in Sympy [A] time = 1.66533, size = 12, normalized size = 0.67 \[ \frac{\left (c + d x\right )^{n + 1}}{d \left (n + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**n,x)
[Out]
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Mathematica [A] time = 0.010218, size = 17, normalized size = 0.94 \[ \frac{(c+d x)^{n+1}}{d n+d} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^n,x]
[Out]
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Maple [A] time = 0.002, size = 19, normalized size = 1.1 \[{\frac{ \left ( dx+c \right ) ^{1+n}}{d \left ( 1+n \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^n,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^n,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217538, size = 27, normalized size = 1.5 \[ \frac{{\left (d x + c\right )}{\left (d x + c\right )}^{n}}{d n + d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^n,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.0396, size = 20, normalized size = 1.11 \[ \frac{\begin{cases} \frac{\left (c + d x\right )^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left (c + d x \right )} & \text{otherwise} \end{cases}}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x+c)**n,x)
[Out]
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GIAC/XCAS [A] time = 0.275069, size = 24, normalized size = 1.33 \[ \frac{{\left (d x + c\right )}^{n + 1}}{d{\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^n,x, algorithm="giac")
[Out]