3.222 \(\int \left (a+b x^3\right )^2 \, dx\)

Optimal. Leaf size=25 \[ a^2 x+\frac{1}{2} a b x^4+\frac{b^2 x^7}{7} \]

[Out]

a^2*x + (a*b*x^4)/2 + (b^2*x^7)/7

_______________________________________________________________________________________

Rubi [A]  time = 0.019294, antiderivative size = 25, 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 \[ a^2 x+\frac{1}{2} a b x^4+\frac{b^2 x^7}{7} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^2,x]

[Out]

a^2*x + (a*b*x^4)/2 + (b^2*x^7)/7

_______________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**2,x)

[Out]

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

_______________________________________________________________________________________

Mathematica [A]  time = 0.00138265, size = 25, normalized size = 1. \[ a^2 x+\frac{1}{2} a b x^4+\frac{b^2 x^7}{7} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^2,x]

[Out]

a^2*x + (a*b*x^4)/2 + (b^2*x^7)/7

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 22, normalized size = 0.9 \[ x{a}^{2}+{\frac{ab{x}^{4}}{2}}+{\frac{{b}^{2}{x}^{7}}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^2,x)

[Out]

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

_______________________________________________________________________________________

Maxima [A]  time = 1.43386, size = 28, normalized size = 1.12 \[ \frac{1}{7} \, b^{2} x^{7} + \frac{1}{2} \, a b x^{4} + a^{2} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*b^2*x^7 + 1/2*a*b*x^4 + a^2*x

_______________________________________________________________________________________

Fricas [A]  time = 0.230754, size = 1, normalized size = 0.04 \[ \frac{1}{7} x^{7} b^{2} + \frac{1}{2} x^{4} b a + x a^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*x^7*b^2 + 1/2*x^4*b*a + x*a^2

_______________________________________________________________________________________

Sympy [A]  time = 0.08248, size = 20, normalized size = 0.8 \[ a^{2} x + \frac{a b x^{4}}{2} + \frac{b^{2} x^{7}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**2,x)

[Out]

a**2*x + a*b*x**4/2 + b**2*x**7/7

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.22073, size = 28, normalized size = 1.12 \[ \frac{1}{7} \, b^{2} x^{7} + \frac{1}{2} \, a b x^{4} + a^{2} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*b^2*x^7 + 1/2*a*b*x^4 + a^2*x