3.87 \(\int \left (2 x+3 x^2\right )^3 \, dx\)

Optimal. Leaf size=25 \[ \frac{27 x^7}{7}+9 x^6+\frac{36 x^5}{5}+2 x^4 \]

[Out]

2*x^4 + (36*x^5)/5 + 9*x^6 + (27*x^7)/7

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Rubi [A]  time = 0.0243206, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{27 x^7}{7}+9 x^6+\frac{36 x^5}{5}+2 x^4 \]

Antiderivative was successfully verified.

[In]  Int[(2*x + 3*x^2)^3,x]

[Out]

2*x^4 + (36*x^5)/5 + 9*x^6 + (27*x^7)/7

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{8 x^{3}}{105} + \frac{\left (6 x + 2\right ) \left (3 x^{2} + 2 x\right )^{3}}{42} - \frac{\left (6 x + 2\right ) \left (3 x^{2} + 2 x\right )^{2}}{105} + \frac{16 \int x\, dx}{105} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3*x**2+2*x)**3,x)

[Out]

8*x**3/105 + (6*x + 2)*(3*x**2 + 2*x)**3/42 - (6*x + 2)*(3*x**2 + 2*x)**2/105 +
16*Integral(x, x)/105

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Mathematica [A]  time = 0.00247379, size = 25, normalized size = 1. \[ \frac{27 x^7}{7}+9 x^6+\frac{36 x^5}{5}+2 x^4 \]

Antiderivative was successfully verified.

[In]  Integrate[(2*x + 3*x^2)^3,x]

[Out]

2*x^4 + (36*x^5)/5 + 9*x^6 + (27*x^7)/7

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Maple [A]  time = 0.002, size = 22, normalized size = 0.9 \[ 2\,{x}^{4}+{\frac{36\,{x}^{5}}{5}}+9\,{x}^{6}+{\frac{27\,{x}^{7}}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3*x^2+2*x)^3,x)

[Out]

2*x^4+36/5*x^5+9*x^6+27/7*x^7

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Maxima [A]  time = 1.33742, size = 28, normalized size = 1.12 \[ \frac{27}{7} \, x^{7} + 9 \, x^{6} + \frac{36}{5} \, x^{5} + 2 \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^2 + 2*x)^3,x, algorithm="maxima")

[Out]

27/7*x^7 + 9*x^6 + 36/5*x^5 + 2*x^4

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Fricas [A]  time = 0.171303, size = 1, normalized size = 0.04 \[ \frac{27}{7} x^{7} + 9 x^{6} + \frac{36}{5} x^{5} + 2 x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^2 + 2*x)^3,x, algorithm="fricas")

[Out]

27/7*x^7 + 9*x^6 + 36/5*x^5 + 2*x^4

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Sympy [A]  time = 0.035019, size = 22, normalized size = 0.88 \[ \frac{27 x^{7}}{7} + 9 x^{6} + \frac{36 x^{5}}{5} + 2 x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x**2+2*x)**3,x)

[Out]

27*x**7/7 + 9*x**6 + 36*x**5/5 + 2*x**4

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GIAC/XCAS [A]  time = 0.220501, size = 28, normalized size = 1.12 \[ \frac{27}{7} \, x^{7} + 9 \, x^{6} + \frac{36}{5} \, x^{5} + 2 \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^2 + 2*x)^3,x, algorithm="giac")

[Out]

27/7*x^7 + 9*x^6 + 36/5*x^5 + 2*x^4