3.292 \(\int x^{7/2} \left (b x^2+c x^4\right ) \, dx\)

Optimal. Leaf size=21 \[ \frac{2}{13} b x^{13/2}+\frac{2}{17} c x^{17/2} \]

[Out]

(2*b*x^(13/2))/13 + (2*c*x^(17/2))/17

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Rubi [A]  time = 0.0140501, 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 \[ \frac{2}{13} b x^{13/2}+\frac{2}{17} c x^{17/2} \]

Antiderivative was successfully verified.

[In]  Int[x^(7/2)*(b*x^2 + c*x^4),x]

[Out]

(2*b*x^(13/2))/13 + (2*c*x^(17/2))/17

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Rubi in Sympy [A]  time = 4.08332, size = 19, normalized size = 0.9 \[ \frac{2 b x^{\frac{13}{2}}}{13} + \frac{2 c x^{\frac{17}{2}}}{17} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(7/2)*(c*x**4+b*x**2),x)

[Out]

2*b*x**(13/2)/13 + 2*c*x**(17/2)/17

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Mathematica [A]  time = 0.0087109, size = 21, normalized size = 1. \[ \frac{2}{13} b x^{13/2}+\frac{2}{17} c x^{17/2} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(7/2)*(b*x^2 + c*x^4),x]

[Out]

(2*b*x^(13/2))/13 + (2*c*x^(17/2))/17

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Maple [A]  time = 0.004, size = 16, normalized size = 0.8 \[{\frac{26\,c{x}^{2}+34\,b}{221}{x}^{{\frac{13}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(7/2)*(c*x^4+b*x^2),x)

[Out]

2/221*x^(13/2)*(13*c*x^2+17*b)

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Maxima [A]  time = 0.678305, size = 18, normalized size = 0.86 \[ \frac{2}{17} \, c x^{\frac{17}{2}} + \frac{2}{13} \, b x^{\frac{13}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*x^(7/2),x, algorithm="maxima")

[Out]

2/17*c*x^(17/2) + 2/13*b*x^(13/2)

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Fricas [A]  time = 0.256989, size = 24, normalized size = 1.14 \[ \frac{2}{221} \,{\left (13 \, c x^{8} + 17 \, b x^{6}\right )} \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*x^(7/2),x, algorithm="fricas")

[Out]

2/221*(13*c*x^8 + 17*b*x^6)*sqrt(x)

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Sympy [A]  time = 34.9266, size = 19, normalized size = 0.9 \[ \frac{2 b x^{\frac{13}{2}}}{13} + \frac{2 c x^{\frac{17}{2}}}{17} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**(7/2)*(c*x**4+b*x**2),x)

[Out]

2*b*x**(13/2)/13 + 2*c*x**(17/2)/17

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GIAC/XCAS [A]  time = 0.269443, size = 18, normalized size = 0.86 \[ \frac{2}{17} \, c x^{\frac{17}{2}} + \frac{2}{13} \, b x^{\frac{13}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)*x^(7/2),x, algorithm="giac")

[Out]

2/17*c*x^(17/2) + 2/13*b*x^(13/2)