Optimal. Leaf size=17 \[ \frac{x^9}{9 a (a+b x)^9} \]
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Rubi [A] time = 0.0016771, antiderivative size = 17, normalized size of antiderivative = 1., 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.
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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 = 0.0272101, size = 97, normalized size = 5.71 \[ -\frac{36 a^6 b^2 x^2+84 a^5 b^3 x^3+126 a^4 b^4 x^4+126 a^3 b^5 x^5+84 a^2 b^6 x^6+9 a^7 b x+a^8+36 a b^7 x^7+9 b^8 x^8}{9 b^9 (a+b x)^9} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 131, normalized size = 7.7 \begin{align*} -14\,{\frac{{a}^{4}}{{b}^{9} \left ( bx+a \right ) ^{5}}}-{\frac{{a}^{8}}{9\,{b}^{9} \left ( bx+a \right ) ^{9}}}-{\frac{1}{{b}^{9} \left ( bx+a \right ) }}+4\,{\frac{a}{{b}^{9} \left ( bx+a \right ) ^{2}}}-4\,{\frac{{a}^{6}}{{b}^{9} \left ( bx+a \right ) ^{7}}}+{\frac{28\,{a}^{5}}{3\,{b}^{9} \left ( bx+a \right ) ^{6}}}+14\,{\frac{{a}^{3}}{{b}^{9} \left ( bx+a \right ) ^{4}}}-{\frac{28\,{a}^{2}}{3\,{b}^{9} \left ( bx+a \right ) ^{3}}}+{\frac{{a}^{7}}{{b}^{9} \left ( bx+a \right ) ^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.10988, size = 251, normalized size = 14.76 \begin{align*} -\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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.43883, size = 404, normalized size = 23.76 \begin{align*} -\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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.64783, size = 199, normalized size = 11.71 \begin{align*} - \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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.21145, size = 128, normalized size = 7.53 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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