3.54 \(\int \left (1+4 x+4 x^2+4 x^4\right ) \, dx\)

Optimal. Leaf size=21 \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

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Rubi [A]  time = 0.00926799, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]

Antiderivative was successfully verified.

[In]  Int[1 + 4*x + 4*x^2 + 4*x^4,x]

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{4 x^{5}}{5} + \frac{4 x^{3}}{3} + x + 4 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(4*x**4+4*x**2+4*x+1,x)

[Out]

4*x**5/5 + 4*x**3/3 + x + 4*Integral(x, x)

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Mathematica [A]  time = 0.000057277, size = 21, normalized size = 1. \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]

Antiderivative was successfully verified.

[In]  Integrate[1 + 4*x + 4*x^2 + 4*x^4,x]

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

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Maple [A]  time = 0.001, size = 18, normalized size = 0.9 \[ x+2\,{x}^{2}+{\frac{4\,{x}^{3}}{3}}+{\frac{4\,{x}^{5}}{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(4*x^4+4*x^2+4*x+1,x)

[Out]

x+2*x^2+4/3*x^3+4/5*x^5

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Maxima [A]  time = 0.808889, size = 23, normalized size = 1.1 \[ \frac{4}{5} \, x^{5} + \frac{4}{3} \, x^{3} + 2 \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(4*x^4 + 4*x^2 + 4*x + 1,x, algorithm="maxima")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x

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Fricas [A]  time = 0.237061, size = 1, normalized size = 0.05 \[ \frac{4}{5} x^{5} + \frac{4}{3} x^{3} + 2 x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(4*x^4 + 4*x^2 + 4*x + 1,x, algorithm="fricas")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x

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Sympy [A]  time = 0.059024, size = 19, normalized size = 0.9 \[ \frac{4 x^{5}}{5} + \frac{4 x^{3}}{3} + 2 x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(4*x**4+4*x**2+4*x+1,x)

[Out]

4*x**5/5 + 4*x**3/3 + 2*x**2 + x

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GIAC/XCAS [A]  time = 0.259678, size = 23, normalized size = 1.1 \[ \frac{4}{5} \, x^{5} + \frac{4}{3} \, x^{3} + 2 \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(4*x^4 + 4*x^2 + 4*x + 1,x, algorithm="giac")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x