3.2 \(\int x^2 \left (x+2 x^2\right )^2 \, dx\)

Optimal. Leaf size=22 \[ \frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5} \]

[Out]

x^5/5 + (2*x^6)/3 + (4*x^7)/7

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Rubi [A]  time = 0.0233712, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5} \]

Antiderivative was successfully verified.

[In]  Int[x^2*(x + 2*x^2)^2,x]

[Out]

x^5/5 + (2*x^6)/3 + (4*x^7)/7

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Rubi in Sympy [A]  time = 2.09129, size = 17, normalized size = 0.77 \[ \frac{4 x^{7}}{7} + \frac{2 x^{6}}{3} + \frac{x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4*x**7/7 + 2*x**6/3 + x**5/5

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Mathematica [A]  time = 0.0057053, size = 22, normalized size = 1. \[ \frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2*(x + 2*x^2)^2,x]

[Out]

x^5/5 + (2*x^6)/3 + (4*x^7)/7

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Maple [A]  time = 0.001, size = 17, normalized size = 0.8 \[{\frac{{x}^{5}}{5}}+{\frac{2\,{x}^{6}}{3}}+{\frac{4\,{x}^{7}}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(2*x^2+x)^2,x)

[Out]

1/5*x^5+2/3*x^6+4/7*x^7

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Maxima [A]  time = 1.36762, size = 22, normalized size = 1. \[ \frac{4}{7} \, x^{7} + \frac{2}{3} \, x^{6} + \frac{1}{5} \, x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/7*x^7 + 2/3*x^6 + 1/5*x^5

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Fricas [A]  time = 0.1694, size = 1, normalized size = 0.05 \[ \frac{4}{7} x^{7} + \frac{2}{3} x^{6} + \frac{1}{5} x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/7*x^7 + 2/3*x^6 + 1/5*x^5

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Sympy [A]  time = 0.032833, size = 17, normalized size = 0.77 \[ \frac{4 x^{7}}{7} + \frac{2 x^{6}}{3} + \frac{x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2*(2*x**2+x)**2,x)

[Out]

4*x**7/7 + 2*x**6/3 + x**5/5

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GIAC/XCAS [A]  time = 0.214127, size = 22, normalized size = 1. \[ \frac{4}{7} \, x^{7} + \frac{2}{3} \, x^{6} + \frac{1}{5} \, x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/7*x^7 + 2/3*x^6 + 1/5*x^5