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 = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, 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 = {45}
\begin {gather*} \frac {a}{9 b^2 (a+b x)^9}-\frac {1}{8 b^2 (a+b x)^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
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*}
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Mathematica [A]
time = 0.00, size = 20, normalized size = 0.67 \begin {gather*} -\frac {a+9 b x}{72 b^2 (a+b x)^9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 27, normalized size = 0.90
method | result | size |
gosper | \(-\frac {9 b x +a}{72 \left (b x +a \right )^{9} b^{2}}\) | \(19\) |
norman | \(\frac {-\frac {x}{8 b}-\frac {a}{72 b^{2}}}{\left (b x +a \right )^{9}}\) | \(22\) |
risch | \(\frac {-\frac {x}{8 b}-\frac {a}{72 b^{2}}}{\left (b x +a \right )^{9}}\) | \(22\) |
default | \(\frac {a}{9 b^{2} \left (b x +a \right )^{9}}-\frac {1}{8 b^{2} \left (b x +a \right )^{8}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 109 vs.
\(2 (26) = 52\).
time = 0.47, size = 109, normalized size = 3.63 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 109 vs.
\(2 (26) = 52\).
time = 0.60, size = 109, normalized size = 3.63 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 116 vs.
\(2 (26) = 52\).
time = 0.27, size = 116, normalized size = 3.87 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.03, size = 18, normalized size = 0.60 \begin {gather*} -\frac {9 \, b x + a}{72 \, {\left (b x + a\right )}^{9} b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 18, normalized size = 0.60 \begin {gather*} -\frac {a+9\,b\,x}{72\,b^2\,{\left (a+b\,x\right )}^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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