3.295 \(\int \sqrt{x} \left (b x^2+c x^4\right ) \, dx\)

Optimal. Leaf size=21 \[ \frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2} \]

[Out]

(2*b*x^(7/2))/7 + (2*c*x^(11/2))/11

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Rubi [A]  time = 0.0138933, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[x]*(b*x^2 + c*x^4),x]

[Out]

(2*b*x^(7/2))/7 + (2*c*x^(11/2))/11

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Rubi in Sympy [A]  time = 4.1029, size = 19, normalized size = 0.9 \[ \frac{2 b x^{\frac{7}{2}}}{7} + \frac{2 c x^{\frac{11}{2}}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(1/2)*(c*x**4+b*x**2),x)

[Out]

2*b*x**(7/2)/7 + 2*c*x**(11/2)/11

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Mathematica [A]  time = 0.00761752, size = 21, normalized size = 1. \[ \frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[x]*(b*x^2 + c*x^4),x]

[Out]

(2*b*x^(7/2))/7 + (2*c*x^(11/2))/11

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Maple [A]  time = 0.004, size = 16, normalized size = 0.8 \[{\frac{14\,c{x}^{2}+22\,b}{77}{x}^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(1/2)*(c*x^4+b*x^2),x)

[Out]

2/77*x^(7/2)*(7*c*x^2+11*b)

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Maxima [A]  time = 0.734461, size = 18, normalized size = 0.86 \[ \frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{7} \, b x^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*sqrt(x),x, algorithm="maxima")

[Out]

2/11*c*x^(11/2) + 2/7*b*x^(7/2)

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Fricas [A]  time = 0.25727, size = 24, normalized size = 1.14 \[ \frac{2}{77} \,{\left (7 \, c x^{5} + 11 \, b x^{3}\right )} \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*sqrt(x),x, algorithm="fricas")

[Out]

2/77*(7*c*x^5 + 11*b*x^3)*sqrt(x)

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Sympy [A]  time = 2.50547, size = 19, normalized size = 0.9 \[ \frac{2 b x^{\frac{7}{2}}}{7} + \frac{2 c x^{\frac{11}{2}}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**(1/2)*(c*x**4+b*x**2),x)

[Out]

2*b*x**(7/2)/7 + 2*c*x**(11/2)/11

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GIAC/XCAS [A]  time = 0.268264, size = 18, normalized size = 0.86 \[ \frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{7} \, b x^{\frac{7}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*sqrt(x),x, algorithm="giac")

[Out]

2/11*c*x^(11/2) + 2/7*b*x^(7/2)