Optimal. Leaf size=17 \[ \frac {x^9}{9 a (a+b x)^9} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {37} \[ \frac {x^9}{9 a (a+b x)^9} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin {align*} \int \frac {x^8}{(a+b x)^{10}} \, dx &=\frac {x^9}{9 a (a+b x)^9}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.02, size = 97, normalized size = 5.71 \[ -\frac {a^8+9 a^7 b x+36 a^6 b^2 x^2+84 a^5 b^3 x^3+126 a^4 b^4 x^4+126 a^3 b^5 x^5+84 a^2 b^6 x^6+36 a b^7 x^7+9 b^8 x^8}{9 b^9 (a+b x)^9} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.45, size = 186, normalized size = 10.94 \[ -\frac {9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, {\left (b^{18} x^{9} + 9 \, a b^{17} x^{8} + 36 \, a^{2} b^{16} x^{7} + 84 \, a^{3} b^{15} x^{6} + 126 \, a^{4} b^{14} x^{5} + 126 \, a^{5} b^{13} x^{4} + 84 \, a^{6} b^{12} x^{3} + 36 \, a^{7} b^{11} x^{2} + 9 \, a^{8} b^{10} x + a^{9} b^{9}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 1.23, size = 95, normalized size = 5.59 \[ -\frac {9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, {\left (b x + a\right )}^{9} b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.01, size = 131, normalized size = 7.71 \[ -\frac {a^{8}}{9 \left (b x +a \right )^{9} b^{9}}+\frac {a^{7}}{\left (b x +a \right )^{8} b^{9}}-\frac {4 a^{6}}{\left (b x +a \right )^{7} b^{9}}+\frac {28 a^{5}}{3 \left (b x +a \right )^{6} b^{9}}-\frac {14 a^{4}}{\left (b x +a \right )^{5} b^{9}}+\frac {14 a^{3}}{\left (b x +a \right )^{4} b^{9}}-\frac {28 a^{2}}{3 \left (b x +a \right )^{3} b^{9}}+\frac {4 a}{\left (b x +a \right )^{2} b^{9}}-\frac {1}{\left (b x +a \right ) b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 1.51, size = 186, normalized size = 10.94 \[ -\frac {9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, {\left (b^{18} x^{9} + 9 \, a b^{17} x^{8} + 36 \, a^{2} b^{16} x^{7} + 84 \, a^{3} b^{15} x^{6} + 126 \, a^{4} b^{14} x^{5} + 126 \, a^{5} b^{13} x^{4} + 84 \, a^{6} b^{12} x^{3} + 36 \, a^{7} b^{11} x^{2} + 9 \, a^{8} b^{10} x + a^{9} b^{9}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.14, size = 107, normalized size = 6.29 \[ -\frac {\frac {1}{a+b\,x}-\frac {4\,a}{{\left (a+b\,x\right )}^2}+\frac {28\,a^2}{3\,{\left (a+b\,x\right )}^3}-\frac {14\,a^3}{{\left (a+b\,x\right )}^4}+\frac {14\,a^4}{{\left (a+b\,x\right )}^5}-\frac {28\,a^5}{3\,{\left (a+b\,x\right )}^6}+\frac {4\,a^6}{{\left (a+b\,x\right )}^7}-\frac {a^7}{{\left (a+b\,x\right )}^8}+\frac {a^8}{9\,{\left (a+b\,x\right )}^9}}{b^9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.98, size = 199, normalized size = 11.71 \[ \frac {- a^{8} - 9 a^{7} b x - 36 a^{6} b^{2} x^{2} - 84 a^{5} b^{3} x^{3} - 126 a^{4} b^{4} x^{4} - 126 a^{3} b^{5} x^{5} - 84 a^{2} b^{6} x^{6} - 36 a b^{7} x^{7} - 9 b^{8} x^{8}}{9 a^{9} b^{9} + 81 a^{8} b^{10} x + 324 a^{7} b^{11} x^{2} + 756 a^{6} b^{12} x^{3} + 1134 a^{5} b^{13} x^{4} + 1134 a^{4} b^{14} x^{5} + 756 a^{3} b^{15} x^{6} + 324 a^{2} b^{16} x^{7} + 81 a b^{17} x^{8} + 9 b^{18} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________