Optimal. Leaf size=80 \[ -\frac{16 b^2 \sqrt{x}}{3 c^3 \sqrt{b x+c x^2}}-\frac{8 b x^{3/2}}{3 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{5/2}}{3 c \sqrt{b x+c x^2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0924031, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{16 b^2 \sqrt{x}}{3 c^3 \sqrt{b x+c x^2}}-\frac{8 b x^{3/2}}{3 c^2 \sqrt{b x+c x^2}}+\frac{2 x^{5/2}}{3 c \sqrt{b x+c x^2}} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)/(b*x + c*x^2)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.25969, size = 73, normalized size = 0.91 \[ - \frac{16 b^{2} \sqrt{x}}{3 c^{3} \sqrt{b x + c x^{2}}} - \frac{8 b x^{\frac{3}{2}}}{3 c^{2} \sqrt{b x + c x^{2}}} + \frac{2 x^{\frac{5}{2}}}{3 c \sqrt{b x + c x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)/(c*x**2+b*x)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.026972, size = 41, normalized size = 0.51 \[ \frac{2 \sqrt{x} \left (-8 b^2-4 b c x+c^2 x^2\right )}{3 c^3 \sqrt{x (b+c x)}} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)/(b*x + c*x^2)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 44, normalized size = 0.6 \[ -{\frac{ \left ( 2\,cx+2\,b \right ) \left ( -{c}^{2}{x}^{2}+4\,bcx+8\,{b}^{2} \right ) }{3\,{c}^{3}}{x}^{{\frac{3}{2}}} \left ( c{x}^{2}+bx \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)/(c*x^2+b*x)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.737561, size = 120, normalized size = 1.5 \[ \frac{2 \,{\left ({\left (c^{3} x^{2} - b c^{2} x - 2 \, b^{2} c\right )} x^{2} - 2 \,{\left (b c^{2} x^{2} + 2 \, b^{2} c x + b^{3}\right )} x\right )}}{3 \,{\left (c^{4} x^{2} + b c^{3} x\right )} \sqrt{c x + b}} - \frac{4 \, b^{2}}{\sqrt{c x + b} c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(7/2)/(c*x^2 + b*x)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.225242, size = 54, normalized size = 0.68 \[ \frac{2 \,{\left (c^{2} x^{3} - 4 \, b c x^{2} - 8 \, b^{2} x\right )}}{3 \, \sqrt{c x^{2} + b x} c^{3} \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(7/2)/(c*x^2 + b*x)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)/(c*x**2+b*x)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.211467, size = 59, normalized size = 0.74 \[ \frac{16 \, b^{\frac{3}{2}}}{3 \, c^{3}} + \frac{2 \,{\left ({\left (c x + b\right )}^{\frac{3}{2}} - 6 \, \sqrt{c x + b} b - \frac{3 \, b^{2}}{\sqrt{c x + b}}\right )}}{3 \, c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(7/2)/(c*x^2 + b*x)^(3/2),x, algorithm="giac")
[Out]