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