Optimal. Leaf size=66 \[ -\frac{a^2}{8 c^2 x^7 \sqrt{c x^2}}-\frac{2 a b}{7 c^2 x^6 \sqrt{c x^2}}-\frac{b^2}{6 c^2 x^5 \sqrt{c x^2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0375986, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{a^2}{8 c^2 x^7 \sqrt{c x^2}}-\frac{2 a b}{7 c^2 x^6 \sqrt{c x^2}}-\frac{b^2}{6 c^2 x^5 \sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^2/(x^4*(c*x^2)^(5/2)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 16.9921, size = 63, normalized size = 0.95 \[ - \frac{a^{2} \sqrt{c x^{2}}}{8 c^{3} x^{9}} - \frac{2 a b \sqrt{c x^{2}}}{7 c^{3} x^{8}} - \frac{b^{2} \sqrt{c x^{2}}}{6 c^{3} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2/x**4/(c*x**2)**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0162651, size = 35, normalized size = 0.53 \[ \frac{-21 a^2-48 a b x-28 b^2 x^2}{168 x^3 \left (c x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^2/(x^4*(c*x^2)^(5/2)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 32, normalized size = 0.5 \[ -{\frac{28\,{b}^{2}{x}^{2}+48\,abx+21\,{a}^{2}}{168\,{x}^{3}} \left ( c{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2/x^4/(c*x^2)^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33033, size = 45, normalized size = 0.68 \[ -\frac{b^{2}}{6 \, c^{\frac{5}{2}} x^{6}} - \frac{2 \, a b}{7 \, c^{\frac{5}{2}} x^{7}} - \frac{a^{2}}{8 \, c^{\frac{5}{2}} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/((c*x^2)^(5/2)*x^4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.208186, size = 46, normalized size = 0.7 \[ -\frac{{\left (28 \, b^{2} x^{2} + 48 \, a b x + 21 \, a^{2}\right )} \sqrt{c x^{2}}}{168 \, c^{3} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/((c*x^2)^(5/2)*x^4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 7.0458, size = 61, normalized size = 0.92 \[ - \frac{a^{2}}{8 c^{\frac{5}{2}} x^{3} \left (x^{2}\right )^{\frac{5}{2}}} - \frac{2 a b}{7 c^{\frac{5}{2}} x^{2} \left (x^{2}\right )^{\frac{5}{2}}} - \frac{b^{2}}{6 c^{\frac{5}{2}} x \left (x^{2}\right )^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**2/x**4/(c*x**2)**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.537897, size = 4, normalized size = 0.06 \[ \mathit{sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/((c*x^2)^(5/2)*x^4),x, algorithm="giac")
[Out]