Integrand size = 13, antiderivative size = 18 \[ \int \frac {3+2 x}{(7+6 x)^3} \, dx=-\frac {(3+2 x)^2}{8 (7+6 x)^2} \]
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Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {37} \[ \int \frac {3+2 x}{(7+6 x)^3} \, dx=-\frac {(2 x+3)^2}{8 (6 x+7)^2} \]
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Rule 37
Rubi steps \begin{align*} \text {integral}& = -\frac {(3+2 x)^2}{8 (7+6 x)^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89 \[ \int \frac {3+2 x}{(7+6 x)^3} \, dx=-\frac {4+3 x}{9 (7+6 x)^2} \]
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Time = 0.03 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78
method | result | size |
norman | \(\frac {-\frac {x}{3}-\frac {4}{9}}{\left (7+6 x \right )^{2}}\) | \(14\) |
gosper | \(-\frac {3 x +4}{9 \left (7+6 x \right )^{2}}\) | \(15\) |
risch | \(\frac {-\frac {x}{3}-\frac {4}{9}}{\left (7+6 x \right )^{2}}\) | \(15\) |
parallelrisch | \(\frac {-12 x -16}{36 \left (7+6 x \right )^{2}}\) | \(15\) |
default | \(-\frac {1}{18 \left (7+6 x \right )}-\frac {1}{18 \left (7+6 x \right )^{2}}\) | \(20\) |
meijerg | \(\frac {3 x \left (\frac {6 x}{7}+2\right )}{686 \left (1+\frac {6 x}{7}\right )^{2}}+\frac {x^{2}}{343 \left (1+\frac {6 x}{7}\right )^{2}}\) | \(29\) |
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none
Time = 0.23 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {3+2 x}{(7+6 x)^3} \, dx=-\frac {3 \, x + 4}{9 \, {\left (36 \, x^{2} + 84 \, x + 49\right )}} \]
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Time = 0.04 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {3+2 x}{(7+6 x)^3} \, dx=\frac {- 3 x - 4}{324 x^{2} + 756 x + 441} \]
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none
Time = 0.18 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {3+2 x}{(7+6 x)^3} \, dx=-\frac {3 \, x + 4}{9 \, {\left (36 \, x^{2} + 84 \, x + 49\right )}} \]
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none
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {3+2 x}{(7+6 x)^3} \, dx=-\frac {3 \, x + 4}{9 \, {\left (6 \, x + 7\right )}^{2}} \]
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Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {3+2 x}{(7+6 x)^3} \, dx=-\frac {3\,x+4}{9\,{\left (6\,x+7\right )}^2} \]
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