Optimal. Leaf size=32 \[ 2^{p-1} (2 x+1) \, _2F_1\left (\frac{1}{2},-p;\frac{3}{2};-\frac{1}{2} (2 x+1)^2\right ) \]
[Out]
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Rubi [A] time = 0.033132, antiderivative size = 32, 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 \[ 2^{p-1} (2 x+1) \, _2F_1\left (\frac{1}{2},-p;\frac{3}{2};-\frac{1}{2} (2 x+1)^2\right ) \]
Antiderivative was successfully verified.
[In] Int[(3 + 4*x + 4*x^2)^p,x]
[Out]
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Rubi in Sympy [A] time = 1.91681, size = 26, normalized size = 0.81 \[ \frac{2^{p} \left (8 x + 4\right ){{}_{2}F_{1}\left (\begin{matrix} - p, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle |{- \frac{\left (8 x + 4\right )^{2}}{32}} \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((4*x**2+4*x+3)**p,x)
[Out]
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Mathematica [C] time = 0.145667, size = 94, normalized size = 2.94 \[ \frac{2^{\frac{3 p}{2}-1} \left (2 x-i \sqrt{2}+1\right ) \left (-2 i x+\sqrt{2}-i\right )^{-p} \left (4 x^2+4 x+3\right )^p \, _2F_1\left (-p,p+1;p+2;\frac{1}{4} \left (2 i \sqrt{2} x+i \sqrt{2}+2\right )\right )}{p+1} \]
Warning: Unable to verify antiderivative.
[In] Integrate[(3 + 4*x + 4*x^2)^p,x]
[Out]
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Maple [F] time = 0.231, size = 0, normalized size = 0. \[ \int \left ( 4\,{x}^{2}+4\,x+3 \right ) ^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((4*x^2+4*x+3)^p,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (4 \, x^{2} + 4 \, x + 3\right )}^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + 4*x + 3)^p,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (4 \, x^{2} + 4 \, x + 3\right )}^{p}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + 4*x + 3)^p,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (4 x^{2} + 4 x + 3\right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x**2+4*x+3)**p,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (4 \, x^{2} + 4 \, x + 3\right )}^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + 4*x + 3)^p,x, algorithm="giac")
[Out]