3.293 \(\int x^{5/2} \left (b x^2+c x^4\right ) \, dx\)

Optimal. Leaf size=21 \[ \frac{2}{11} b x^{11/2}+\frac{2}{15} c x^{15/2} \]

[Out]

(2*b*x^(11/2))/11 + (2*c*x^(15/2))/15

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Rubi [A]  time = 0.0139778, 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 \[ \frac{2}{11} b x^{11/2}+\frac{2}{15} c x^{15/2} \]

Antiderivative was successfully verified.

[In]  Int[x^(5/2)*(b*x^2 + c*x^4),x]

[Out]

(2*b*x^(11/2))/11 + (2*c*x^(15/2))/15

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Rubi in Sympy [A]  time = 4.1525, size = 19, normalized size = 0.9 \[ \frac{2 b x^{\frac{11}{2}}}{11} + \frac{2 c x^{\frac{15}{2}}}{15} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(5/2)*(c*x**4+b*x**2),x)

[Out]

2*b*x**(11/2)/11 + 2*c*x**(15/2)/15

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Mathematica [A]  time = 0.00774103, size = 21, normalized size = 1. \[ \frac{2}{11} b x^{11/2}+\frac{2}{15} c x^{15/2} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(5/2)*(b*x^2 + c*x^4),x]

[Out]

(2*b*x^(11/2))/11 + (2*c*x^(15/2))/15

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Maple [A]  time = 0.004, size = 16, normalized size = 0.8 \[{\frac{22\,c{x}^{2}+30\,b}{165}{x}^{{\frac{11}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(5/2)*(c*x^4+b*x^2),x)

[Out]

2/165*x^(11/2)*(11*c*x^2+15*b)

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Maxima [A]  time = 0.684087, size = 18, normalized size = 0.86 \[ \frac{2}{15} \, c x^{\frac{15}{2}} + \frac{2}{11} \, b x^{\frac{11}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*x^(5/2),x, algorithm="maxima")

[Out]

2/15*c*x^(15/2) + 2/11*b*x^(11/2)

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Fricas [A]  time = 0.260159, size = 24, normalized size = 1.14 \[ \frac{2}{165} \,{\left (11 \, c x^{7} + 15 \, b x^{5}\right )} \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*x^(5/2),x, algorithm="fricas")

[Out]

2/165*(11*c*x^7 + 15*b*x^5)*sqrt(x)

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Sympy [A]  time = 17.0236, size = 19, normalized size = 0.9 \[ \frac{2 b x^{\frac{11}{2}}}{11} + \frac{2 c x^{\frac{15}{2}}}{15} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**(5/2)*(c*x**4+b*x**2),x)

[Out]

2*b*x**(11/2)/11 + 2*c*x**(15/2)/15

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GIAC/XCAS [A]  time = 0.26639, size = 18, normalized size = 0.86 \[ \frac{2}{15} \, c x^{\frac{15}{2}} + \frac{2}{11} \, b x^{\frac{11}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*x^(5/2),x, algorithm="giac")

[Out]

2/15*c*x^(15/2) + 2/11*b*x^(11/2)