Optimal. Leaf size=40 \[ \frac{b \left (a+b x^2\right )^6}{84 a^2 x^{12}}-\frac{\left (a+b x^2\right )^6}{14 a x^{14}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0581051, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{b \left (a+b x^2\right )^6}{84 a^2 x^{12}}-\frac{\left (a+b x^2\right )^6}{14 a x^{14}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^5/x^15,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.4845, size = 32, normalized size = 0.8 \[ - \frac{\left (a + b x^{2}\right )^{6}}{14 a x^{14}} + \frac{b \left (a + b x^{2}\right )^{6}}{84 a^{2} x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**5/x**15,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0110855, size = 67, normalized size = 1.68 \[ -\frac{a^5}{14 x^{14}}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^3 b^2}{x^{10}}-\frac{5 a^2 b^3}{4 x^8}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^5/x^15,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 58, normalized size = 1.5 \[ -{\frac{5\,{a}^{4}b}{12\,{x}^{12}}}-{\frac{5\,a{b}^{4}}{6\,{x}^{6}}}-{\frac{{b}^{5}}{4\,{x}^{4}}}-{\frac{5\,{a}^{2}{b}^{3}}{4\,{x}^{8}}}-{\frac{{a}^{5}}{14\,{x}^{14}}}-{\frac{{a}^{3}{b}^{2}}{{x}^{10}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^5/x^15,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33184, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{10} + 70 \, a b^{4} x^{8} + 105 \, a^{2} b^{3} x^{6} + 84 \, a^{3} b^{2} x^{4} + 35 \, a^{4} b x^{2} + 6 \, a^{5}}{84 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5/x^15,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.207042, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{10} + 70 \, a b^{4} x^{8} + 105 \, a^{2} b^{3} x^{6} + 84 \, a^{3} b^{2} x^{4} + 35 \, a^{4} b x^{2} + 6 \, a^{5}}{84 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5/x^15,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.48686, size = 63, normalized size = 1.58 \[ - \frac{6 a^{5} + 35 a^{4} b x^{2} + 84 a^{3} b^{2} x^{4} + 105 a^{2} b^{3} x^{6} + 70 a b^{4} x^{8} + 21 b^{5} x^{10}}{84 x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**5/x**15,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.206607, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{10} + 70 \, a b^{4} x^{8} + 105 \, a^{2} b^{3} x^{6} + 84 \, a^{3} b^{2} x^{4} + 35 \, a^{4} b x^{2} + 6 \, a^{5}}{84 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5/x^15,x, algorithm="giac")
[Out]