3.252 \(\int \left (a+b x^3\right )^3 \, dx\)

Optimal. Leaf size=38 \[ a^3 x+\frac{3}{4} a^2 b x^4+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10} \]

[Out]

a^3*x + (3*a^2*b*x^4)/4 + (3*a*b^2*x^7)/7 + (b^3*x^10)/10

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Rubi [A]  time = 0.0275176, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ a^3 x+\frac{3}{4} a^2 b x^4+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^3,x]

[Out]

a^3*x + (3*a^2*b*x^4)/4 + (3*a*b^2*x^7)/7 + (b^3*x^10)/10

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{10}}{10} + \int a^{3}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**3,x)

[Out]

3*a**2*b*x**4/4 + 3*a*b**2*x**7/7 + b**3*x**10/10 + Integral(a**3, x)

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Mathematica [A]  time = 0.00176727, size = 38, normalized size = 1. \[ a^3 x+\frac{3}{4} a^2 b x^4+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^3,x]

[Out]

a^3*x + (3*a^2*b*x^4)/4 + (3*a*b^2*x^7)/7 + (b^3*x^10)/10

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Maple [A]  time = 0.001, size = 33, normalized size = 0.9 \[{a}^{3}x+{\frac{3\,{a}^{2}b{x}^{4}}{4}}+{\frac{3\,a{b}^{2}{x}^{7}}{7}}+{\frac{{b}^{3}{x}^{10}}{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^3,x)

[Out]

a^3*x+3/4*a^2*b*x^4+3/7*a*b^2*x^7+1/10*b^3*x^10

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Maxima [A]  time = 1.43028, size = 43, normalized size = 1.13 \[ \frac{1}{10} \, b^{3} x^{10} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{4} \, a^{2} b x^{4} + a^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*b^3*x^10 + 3/7*a*b^2*x^7 + 3/4*a^2*b*x^4 + a^3*x

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Fricas [A]  time = 0.189061, size = 1, normalized size = 0.03 \[ \frac{1}{10} x^{10} b^{3} + \frac{3}{7} x^{7} b^{2} a + \frac{3}{4} x^{4} b a^{2} + x a^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*x^10*b^3 + 3/7*x^7*b^2*a + 3/4*x^4*b*a^2 + x*a^3

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Sympy [A]  time = 0.091346, size = 36, normalized size = 0.95 \[ a^{3} x + \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{10}}{10} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**3,x)

[Out]

a**3*x + 3*a**2*b*x**4/4 + 3*a*b**2*x**7/7 + b**3*x**10/10

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GIAC/XCAS [A]  time = 0.215539, size = 43, normalized size = 1.13 \[ \frac{1}{10} \, b^{3} x^{10} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{4} \, a^{2} b x^{4} + a^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*b^3*x^10 + 3/7*a*b^2*x^7 + 3/4*a^2*b*x^4 + a^3*x