Optimal. Leaf size=58 \[ \frac{x^{14}}{504 a^3 \left (a+b x^2\right )^7}+\frac{x^{14}}{72 a^2 \left (a+b x^2\right )^8}+\frac{x^{14}}{18 a \left (a+b x^2\right )^9} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0814398, antiderivative size = 58, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{x^{14}}{504 a^3 \left (a+b x^2\right )^7}+\frac{x^{14}}{72 a^2 \left (a+b x^2\right )^8}+\frac{x^{14}}{18 a \left (a+b x^2\right )^9} \]
Antiderivative was successfully verified.
[In] Int[x^13/(a + b*x^2)^10,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.86219, size = 48, normalized size = 0.83 \[ \frac{x^{14}}{18 a \left (a + b x^{2}\right )^{9}} + \frac{x^{14}}{72 a^{2} \left (a + b x^{2}\right )^{8}} + \frac{x^{14}}{504 a^{3} \left (a + b x^{2}\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**13/(b*x**2+a)**10,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.031869, size = 79, normalized size = 1.36 \[ -\frac{a^6+9 a^5 b x^2+36 a^4 b^2 x^4+84 a^3 b^3 x^6+126 a^2 b^4 x^8+126 a b^5 x^{10}+84 b^6 x^{12}}{504 b^7 \left (a+b x^2\right )^9} \]
Antiderivative was successfully verified.
[In] Integrate[x^13/(a + b*x^2)^10,x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.014, size = 116, normalized size = 2. \[ -{\frac{3\,{a}^{2}}{2\,{b}^{7} \left ( b{x}^{2}+a \right ) ^{5}}}-{\frac{{a}^{6}}{18\,{b}^{7} \left ( b{x}^{2}+a \right ) ^{9}}}-{\frac{1}{6\, \left ( b{x}^{2}+a \right ) ^{3}{b}^{7}}}-{\frac{15\,{a}^{4}}{14\,{b}^{7} \left ( b{x}^{2}+a \right ) ^{7}}}+{\frac{5\,{a}^{3}}{3\,{b}^{7} \left ( b{x}^{2}+a \right ) ^{6}}}+{\frac{3\,{a}^{5}}{8\,{b}^{7} \left ( b{x}^{2}+a \right ) ^{8}}}+{\frac{3\,a}{4\,{b}^{7} \left ( b{x}^{2}+a \right ) ^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^13/(b*x^2+a)^10,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34643, size = 227, normalized size = 3.91 \[ -\frac{84 \, b^{6} x^{12} + 126 \, a b^{5} x^{10} + 126 \, a^{2} b^{4} x^{8} + 84 \, a^{3} b^{3} x^{6} + 36 \, a^{4} b^{2} x^{4} + 9 \, a^{5} b x^{2} + a^{6}}{504 \,{\left (b^{16} x^{18} + 9 \, a b^{15} x^{16} + 36 \, a^{2} b^{14} x^{14} + 84 \, a^{3} b^{13} x^{12} + 126 \, a^{4} b^{12} x^{10} + 126 \, a^{5} b^{11} x^{8} + 84 \, a^{6} b^{10} x^{6} + 36 \, a^{7} b^{9} x^{4} + 9 \, a^{8} b^{8} x^{2} + a^{9} b^{7}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^13/(b*x^2 + a)^10,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.204256, size = 227, normalized size = 3.91 \[ -\frac{84 \, b^{6} x^{12} + 126 \, a b^{5} x^{10} + 126 \, a^{2} b^{4} x^{8} + 84 \, a^{3} b^{3} x^{6} + 36 \, a^{4} b^{2} x^{4} + 9 \, a^{5} b x^{2} + a^{6}}{504 \,{\left (b^{16} x^{18} + 9 \, a b^{15} x^{16} + 36 \, a^{2} b^{14} x^{14} + 84 \, a^{3} b^{13} x^{12} + 126 \, a^{4} b^{12} x^{10} + 126 \, a^{5} b^{11} x^{8} + 84 \, a^{6} b^{10} x^{6} + 36 \, a^{7} b^{9} x^{4} + 9 \, a^{8} b^{8} x^{2} + a^{9} b^{7}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^13/(b*x^2 + a)^10,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 34.8363, size = 178, normalized size = 3.07 \[ - \frac{a^{6} + 9 a^{5} b x^{2} + 36 a^{4} b^{2} x^{4} + 84 a^{3} b^{3} x^{6} + 126 a^{2} b^{4} x^{8} + 126 a b^{5} x^{10} + 84 b^{6} x^{12}}{504 a^{9} b^{7} + 4536 a^{8} b^{8} x^{2} + 18144 a^{7} b^{9} x^{4} + 42336 a^{6} b^{10} x^{6} + 63504 a^{5} b^{11} x^{8} + 63504 a^{4} b^{12} x^{10} + 42336 a^{3} b^{13} x^{12} + 18144 a^{2} b^{14} x^{14} + 4536 a b^{15} x^{16} + 504 b^{16} x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**13/(b*x**2+a)**10,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209252, size = 104, normalized size = 1.79 \[ -\frac{84 \, b^{6} x^{12} + 126 \, a b^{5} x^{10} + 126 \, a^{2} b^{4} x^{8} + 84 \, a^{3} b^{3} x^{6} + 36 \, a^{4} b^{2} x^{4} + 9 \, a^{5} b x^{2} + a^{6}}{504 \,{\left (b x^{2} + a\right )}^{9} b^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^13/(b*x^2 + a)^10,x, algorithm="giac")
[Out]