Optimal. Leaf size=41 \[ -\frac{c^3}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0671049, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 32, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{c^3}{2 e (d+e x) \sqrt{c d^2+2 c d e x+c e^2 x^2}} \]
Antiderivative was successfully verified.
[In] Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^8,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 17.9061, size = 36, normalized size = 0.88 \[ - \frac{\left (c d^{2} + 2 c d e x + c e^{2} x^{2}\right )^{\frac{5}{2}}}{2 e \left (d + e x\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**8,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0221201, size = 27, normalized size = 0.66 \[ -\frac{\left (c (d+e x)^2\right )^{5/2}}{2 e (d+e x)^7} \]
Antiderivative was successfully verified.
[In] Integrate[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^8,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 35, normalized size = 0.9 \[ -{\frac{1}{2\, \left ( ex+d \right ) ^{7}e} \left ( c{e}^{2}{x}^{2}+2\,cdex+c{d}^{2} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^8,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^(5/2)/(e*x + d)^8,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218506, size = 81, normalized size = 1.98 \[ -\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c^{2}}{2 \,{\left (e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^(5/2)/(e*x + d)^8,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c \left (d + e x\right )^{2}\right )^{\frac{5}{2}}}{\left (d + e x\right )^{8}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e**2*x**2+2*c*d*e*x+c*d**2)**(5/2)/(e*x+d)**8,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.773867, size = 1, normalized size = 0.02 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^(5/2)/(e*x + d)^8,x, algorithm="giac")
[Out]