3.651 \(\int x^{4/3} (a+b x) \, dx\)

Optimal. Leaf size=21 \[ \frac{3}{7} a x^{7/3}+\frac{3}{10} b x^{10/3} \]

[Out]

(3*a*x^(7/3))/7 + (3*b*x^(10/3))/10

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Rubi [A]  time = 0.0130831, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{3}{7} a x^{7/3}+\frac{3}{10} b x^{10/3} \]

Antiderivative was successfully verified.

[In]  Int[x^(4/3)*(a + b*x),x]

[Out]

(3*a*x^(7/3))/7 + (3*b*x^(10/3))/10

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Rubi in Sympy [A]  time = 2.35771, size = 19, normalized size = 0.9 \[ \frac{3 a x^{\frac{7}{3}}}{7} + \frac{3 b x^{\frac{10}{3}}}{10} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(4/3)*(b*x+a),x)

[Out]

3*a*x**(7/3)/7 + 3*b*x**(10/3)/10

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Mathematica [A]  time = 0.00552099, size = 17, normalized size = 0.81 \[ \frac{3}{70} x^{7/3} (10 a+7 b x) \]

Antiderivative was successfully verified.

[In]  Integrate[x^(4/3)*(a + b*x),x]

[Out]

(3*x^(7/3)*(10*a + 7*b*x))/70

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Maple [A]  time = 0.003, size = 14, normalized size = 0.7 \[{\frac{21\,bx+30\,a}{70}{x}^{{\frac{7}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(4/3)*(b*x+a),x)

[Out]

3/70*x^(7/3)*(7*b*x+10*a)

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Maxima [A]  time = 1.34989, size = 18, normalized size = 0.86 \[ \frac{3}{10} \, b x^{\frac{10}{3}} + \frac{3}{7} \, a x^{\frac{7}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)*x^(4/3),x, algorithm="maxima")

[Out]

3/10*b*x^(10/3) + 3/7*a*x^(7/3)

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Fricas [A]  time = 0.205048, size = 24, normalized size = 1.14 \[ \frac{3}{70} \,{\left (7 \, b x^{3} + 10 \, a x^{2}\right )} x^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)*x^(4/3),x, algorithm="fricas")

[Out]

3/70*(7*b*x^3 + 10*a*x^2)*x^(1/3)

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Sympy [A]  time = 2.58819, size = 19, normalized size = 0.9 \[ \frac{3 a x^{\frac{7}{3}}}{7} + \frac{3 b x^{\frac{10}{3}}}{10} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**(4/3)*(b*x+a),x)

[Out]

3*a*x**(7/3)/7 + 3*b*x**(10/3)/10

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GIAC/XCAS [A]  time = 0.204476, size = 18, normalized size = 0.86 \[ \frac{3}{10} \, b x^{\frac{10}{3}} + \frac{3}{7} \, a x^{\frac{7}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)*x^(4/3),x, algorithm="giac")

[Out]

3/10*b*x^(10/3) + 3/7*a*x^(7/3)