Optimal. Leaf size=30 \[ \frac{a}{9 b^2 (a+b x)^9}-\frac{1}{8 b^2 (a+b x)^8} \]
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Rubi [A] time = 0.0135037, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ \frac{a}{9 b^2 (a+b x)^9}-\frac{1}{8 b^2 (a+b x)^8} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{x}{(a+b x)^{10}} \, dx &=\int \left (-\frac{a}{b (a+b x)^{10}}+\frac{1}{b (a+b x)^9}\right ) \, dx\\ &=\frac{a}{9 b^2 (a+b x)^9}-\frac{1}{8 b^2 (a+b x)^8}\\ \end{align*}
Mathematica [A] time = 0.0091609, size = 20, normalized size = 0.67 \[ -\frac{a+9 b x}{72 b^2 (a+b x)^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.9 \begin{align*}{\frac{a}{9\,{b}^{2} \left ( bx+a \right ) ^{9}}}-{\frac{1}{8\,{b}^{2} \left ( bx+a \right ) ^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.17228, size = 147, normalized size = 4.9 \begin{align*} -\frac{9 \, b x + a}{72 \,{\left (b^{11} x^{9} + 9 \, a b^{10} x^{8} + 36 \, a^{2} b^{9} x^{7} + 84 \, a^{3} b^{8} x^{6} + 126 \, a^{4} b^{7} x^{5} + 126 \, a^{5} b^{6} x^{4} + 84 \, a^{6} b^{5} x^{3} + 36 \, a^{7} b^{4} x^{2} + 9 \, a^{8} b^{3} x + a^{9} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.38064, size = 234, normalized size = 7.8 \begin{align*} -\frac{9 \, b x + a}{72 \,{\left (b^{11} x^{9} + 9 \, a b^{10} x^{8} + 36 \, a^{2} b^{9} x^{7} + 84 \, a^{3} b^{8} x^{6} + 126 \, a^{4} b^{7} x^{5} + 126 \, a^{5} b^{6} x^{4} + 84 \, a^{6} b^{5} x^{3} + 36 \, a^{7} b^{4} x^{2} + 9 \, a^{8} b^{3} x + a^{9} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.07181, size = 116, normalized size = 3.87 \begin{align*} - \frac{a + 9 b x}{72 a^{9} b^{2} + 648 a^{8} b^{3} x + 2592 a^{7} b^{4} x^{2} + 6048 a^{6} b^{5} x^{3} + 9072 a^{5} b^{6} x^{4} + 9072 a^{4} b^{7} x^{5} + 6048 a^{3} b^{8} x^{6} + 2592 a^{2} b^{9} x^{7} + 648 a b^{10} x^{8} + 72 b^{11} x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20915, size = 24, normalized size = 0.8 \begin{align*} -\frac{9 \, b x + a}{72 \,{\left (b x + a\right )}^{9} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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