Optimal. Leaf size=64 \[ \frac{a^3}{9 b^4 (a+b x)^9}-\frac{3 a^2}{8 b^4 (a+b x)^8}+\frac{3 a}{7 b^4 (a+b x)^7}-\frac{1}{6 b^4 (a+b x)^6} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0714916, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a^3}{9 b^4 (a+b x)^9}-\frac{3 a^2}{8 b^4 (a+b x)^8}+\frac{3 a}{7 b^4 (a+b x)^7}-\frac{1}{6 b^4 (a+b x)^6} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a + b*x)^10,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 14.3559, size = 60, normalized size = 0.94 \[ \frac{a^{3}}{9 b^{4} \left (a + b x\right )^{9}} - \frac{3 a^{2}}{8 b^{4} \left (a + b x\right )^{8}} + \frac{3 a}{7 b^{4} \left (a + b x\right )^{7}} - \frac{1}{6 b^{4} \left (a + b x\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(b*x+a)**10,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0141554, size = 42, normalized size = 0.66 \[ -\frac{a^3+9 a^2 b x+36 a b^2 x^2+84 b^3 x^3}{504 b^4 (a+b x)^9} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a + b*x)^10,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 57, normalized size = 0.9 \[{\frac{{a}^{3}}{9\,{b}^{4} \left ( bx+a \right ) ^{9}}}-{\frac{3\,{a}^{2}}{8\,{b}^{4} \left ( bx+a \right ) ^{8}}}+{\frac{3\,a}{7\,{b}^{4} \left ( bx+a \right ) ^{7}}}-{\frac{1}{6\,{b}^{4} \left ( bx+a \right ) ^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(b*x+a)^10,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33597, size = 177, normalized size = 2.77 \[ -\frac{84 \, b^{3} x^{3} + 36 \, a b^{2} x^{2} + 9 \, a^{2} b x + a^{3}}{504 \,{\left (b^{13} x^{9} + 9 \, a b^{12} x^{8} + 36 \, a^{2} b^{11} x^{7} + 84 \, a^{3} b^{10} x^{6} + 126 \, a^{4} b^{9} x^{5} + 126 \, a^{5} b^{8} x^{4} + 84 \, a^{6} b^{7} x^{3} + 36 \, a^{7} b^{6} x^{2} + 9 \, a^{8} b^{5} x + a^{9} b^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^10,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.211935, size = 177, normalized size = 2.77 \[ -\frac{84 \, b^{3} x^{3} + 36 \, a b^{2} x^{2} + 9 \, a^{2} b x + a^{3}}{504 \,{\left (b^{13} x^{9} + 9 \, a b^{12} x^{8} + 36 \, a^{2} b^{11} x^{7} + 84 \, a^{3} b^{10} x^{6} + 126 \, a^{4} b^{9} x^{5} + 126 \, a^{5} b^{8} x^{4} + 84 \, a^{6} b^{7} x^{3} + 36 \, a^{7} b^{6} x^{2} + 9 \, a^{8} b^{5} x + a^{9} b^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^10,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.27566, size = 139, normalized size = 2.17 \[ - \frac{a^{3} + 9 a^{2} b x + 36 a b^{2} x^{2} + 84 b^{3} x^{3}}{504 a^{9} b^{4} + 4536 a^{8} b^{5} x + 18144 a^{7} b^{6} x^{2} + 42336 a^{6} b^{7} x^{3} + 63504 a^{5} b^{8} x^{4} + 63504 a^{4} b^{9} x^{5} + 42336 a^{3} b^{10} x^{6} + 18144 a^{2} b^{11} x^{7} + 4536 a b^{12} x^{8} + 504 b^{13} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(b*x+a)**10,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.203175, size = 54, normalized size = 0.84 \[ -\frac{84 \, b^{3} x^{3} + 36 \, a b^{2} x^{2} + 9 \, a^{2} b x + a^{3}}{504 \,{\left (b x + a\right )}^{9} b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x + a)^10,x, algorithm="giac")
[Out]