Optimal. Leaf size=18 \[ \frac{(a+b x)^{n+1}}{b (n+1)} \]
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Rubi [A] time = 0.010586, 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 \[ \frac{(a+b x)^{n+1}}{b (n+1)} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^n,x]
[Out]
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Rubi in Sympy [A] time = 1.73676, size = 12, normalized size = 0.67 \[ \frac{\left (a + b x\right )^{n + 1}}{b \left (n + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**n,x)
[Out]
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Mathematica [A] time = 0.00967821, size = 17, normalized size = 0.94 \[ \frac{(a+b x)^{n+1}}{b n+b} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^n,x]
[Out]
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Maple [A] time = 0.003, size = 19, normalized size = 1.1 \[{\frac{ \left ( bx+a \right ) ^{1+n}}{b \left ( 1+n \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^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((b*x + a)^n,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222127, size = 27, normalized size = 1.5 \[ \frac{{\left (b x + a\right )}{\left (b x + a\right )}^{n}}{b n + b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^n,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.081347, size = 20, normalized size = 1.11 \[ \frac{\begin{cases} \frac{\left (a + b x\right )^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left (a + b x \right )} & \text{otherwise} \end{cases}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**n,x)
[Out]
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GIAC/XCAS [A] time = 0.20329, size = 24, normalized size = 1.33 \[ \frac{{\left (b x + a\right )}^{n + 1}}{b{\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^n,x, algorithm="giac")
[Out]