Optimal. Leaf size=31 \[ -7^p (2-x) \, _2F_1\left (\frac{1}{2},-p;\frac{3}{2};\frac{1}{7} (2-x)^2\right ) \]
[Out]
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Rubi [A] time = 0.0279102, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ -7^p (2-x) \, _2F_1\left (\frac{1}{2},-p;\frac{3}{2};\frac{1}{7} (2-x)^2\right ) \]
Antiderivative was successfully verified.
[In] Int[(3 + 4*x - x^2)^p,x]
[Out]
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Rubi in Sympy [A] time = 1.95643, size = 26, normalized size = 0.84 \[ - \frac{7^{p} \left (- 2 x + 4\right ){{}_{2}F_{1}\left (\begin{matrix} - p, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle |{\frac{\left (- 2 x + 4\right )^{2}}{28}} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**2+4*x+3)**p,x)
[Out]
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Mathematica [B] time = 0.0801263, size = 83, normalized size = 2.68 \[ -\frac{\left (-x+\sqrt{7}+2\right ) \left (-x^2+4 x+3\right )^p \left (\frac{x-\sqrt{7}-2}{2 \sqrt{7}}+1\right )^{-p} \, _2F_1\left (-p,p+1;p+2;-\frac{x-\sqrt{7}-2}{2 \sqrt{7}}\right )}{p+1} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 4*x - x^2)^p,x]
[Out]
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Maple [F] time = 0.151, size = 0, normalized size = 0. \[ \int \left ( -{x}^{2}+4\,x+3 \right ) ^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^2+4*x+3)^p,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (-x^{2} + 4 \, x + 3\right )}^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^2 + 4*x + 3)^p,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (-x^{2} + 4 \, x + 3\right )}^{p}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^2 + 4*x + 3)^p,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (- x^{2} + 4 x + 3\right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**2+4*x+3)**p,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (-x^{2} + 4 \, x + 3\right )}^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^2 + 4*x + 3)^p,x, algorithm="giac")
[Out]