Optimal. Leaf size=32 \[ \frac{c \left (c d^2+2 c d e x+c e^2 x^2\right )^{3/2}}{3 e} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0657981, antiderivative size = 32, 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 \[ \frac{c \left (c d^2+2 c d e x+c e^2 x^2\right )^{3/2}}{3 e} \]
Antiderivative was successfully verified.
[In] Int[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 17.6832, size = 29, normalized size = 0.91 \[ \frac{c \left (c d^{2} + 2 c d e x + c e^{2} x^{2}\right )^{\frac{3}{2}}}{3 e} \]
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)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0180067, size = 21, normalized size = 0.66 \[ \frac{c \left (c (d+e x)^2\right )^{3/2}}{3 e} \]
Antiderivative was successfully verified.
[In] Integrate[(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 51, normalized size = 1.6 \[{\frac{x \left ({e}^{2}{x}^{2}+3\,dex+3\,{d}^{2} \right ) }{3\, \left ( ex+d \right ) ^{5}} \left ( c{e}^{2}{x}^{2}+2\,cdex+c{d}^{2} \right ) ^{{\frac{5}{2}}}} \]
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)^3,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)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.226685, size = 82, normalized size = 2.56 \[ \frac{{\left (c^{2} e^{2} x^{3} + 3 \, c^{2} d e x^{2} + 3 \, c^{2} d^{2} x\right )} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{3 \,{\left (e x + d\right )}} \]
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)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c \left (d + e x\right )^{2}\right )^{\frac{5}{2}}}{\left (d + e x\right )^{3}}\, dx \]
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)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.317267, size = 1, normalized size = 0.03 \[ \mathit{Done} \]
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)^3,x, algorithm="giac")
[Out]