Optimal. Leaf size=18 \[ \frac{(4 x+3)^{p+1}}{4 (p+1)} \]
[Out]
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Rubi [A] time = 0.00803477, 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 \[ \frac{(4 x+3)^{p+1}}{4 (p+1)} \]
Antiderivative was successfully verified.
[In] Int[(3 + 4*x)^p,x]
[Out]
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Rubi in Sympy [A] time = 1.48413, size = 12, normalized size = 0.67 \[ \frac{\left (4 x + 3\right )^{p + 1}}{4 \left (p + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+4*x)**p,x)
[Out]
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Mathematica [A] time = 0.00842931, size = 17, normalized size = 0.94 \[ \frac{(4 x+3)^{p+1}}{4 p+4} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 4*x)^p,x]
[Out]
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Maple [A] time = 0.003, size = 17, normalized size = 0.9 \[{\frac{ \left ( 3+4\,x \right ) ^{1+p}}{4\,p+4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+4*x)^p,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((4*x + 3)^p,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235928, size = 26, normalized size = 1.44 \[ \frac{{\left (4 \, x + 3\right )}^{p}{\left (4 \, x + 3\right )}}{4 \,{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x + 3)^p,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.073729, size = 20, normalized size = 1.11 \[ \frac{\begin{cases} \frac{\left (4 x + 3\right )^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left (4 x + 3 \right )} & \text{otherwise} \end{cases}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+4*x)**p,x)
[Out]
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GIAC/XCAS [A] time = 0.206089, size = 22, normalized size = 1.22 \[ \frac{{\left (4 \, x + 3\right )}^{p + 1}}{4 \,{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x + 3)^p,x, algorithm="giac")
[Out]