Integrand size = 36, antiderivative size = 20 \[ \int \frac {(3+x)^3 \left (30-68 x+30 x^2-4 x^3\right )}{27-9 x-3 x^2+x^3} \, dx=\left (3-\frac {2}{3-x}-x\right ) (3+x)^3 \]
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Time = 0.04 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.40, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {1600, 27, 1634} \[ \int \frac {(3+x)^3 \left (30-68 x+30 x^2-4 x^3\right )}{27-9 x-3 x^2+x^3} \, dx=-x^4-6 x^3+2 x^2+78 x-\frac {432}{3-x} \]
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Rule 27
Rule 1600
Rule 1634
Rubi steps \begin{align*} \text {integral}& = \int \frac {(3+x)^2 \left (30-68 x+30 x^2-4 x^3\right )}{9-6 x+x^2} \, dx \\ & = \int \frac {(3+x)^2 \left (30-68 x+30 x^2-4 x^3\right )}{(-3+x)^2} \, dx \\ & = \int \left (78-\frac {432}{(-3+x)^2}+4 x-18 x^2-4 x^3\right ) \, dx \\ & = -\frac {432}{3-x}+78 x+2 x^2-6 x^3-x^4 \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.50 \[ \int \frac {(3+x)^3 \left (30-68 x+30 x^2-4 x^3\right )}{27-9 x-3 x^2+x^3} \, dx=-\frac {-459+243 x-72 x^2-20 x^3+3 x^4+x^5}{-3+x} \]
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Time = 0.27 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.35
method | result | size |
default | \(-x^{4}-6 x^{3}+2 x^{2}+78 x +\frac {432}{-3+x}\) | \(27\) |
risch | \(-x^{4}-6 x^{3}+2 x^{2}+78 x +\frac {432}{-3+x}\) | \(27\) |
gosper | \(-\frac {x^{5}+3 x^{4}-20 x^{3}-72 x^{2}+270}{-3+x}\) | \(28\) |
parallelrisch | \(-\frac {x^{5}+3 x^{4}-20 x^{3}-72 x^{2}+270}{-3+x}\) | \(28\) |
norman | \(\frac {-x^{5}-3 x^{4}+20 x^{3}+72 x^{2}-270}{-3+x}\) | \(29\) |
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none
Time = 0.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.50 \[ \int \frac {(3+x)^3 \left (30-68 x+30 x^2-4 x^3\right )}{27-9 x-3 x^2+x^3} \, dx=-\frac {x^{5} + 3 \, x^{4} - 20 \, x^{3} - 72 \, x^{2} + 234 \, x - 432}{x - 3} \]
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Time = 0.05 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {(3+x)^3 \left (30-68 x+30 x^2-4 x^3\right )}{27-9 x-3 x^2+x^3} \, dx=- x^{4} - 6 x^{3} + 2 x^{2} + 78 x + \frac {432}{x - 3} \]
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none
Time = 0.18 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30 \[ \int \frac {(3+x)^3 \left (30-68 x+30 x^2-4 x^3\right )}{27-9 x-3 x^2+x^3} \, dx=-x^{4} - 6 \, x^{3} + 2 \, x^{2} + 78 \, x + \frac {432}{x - 3} \]
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none
Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30 \[ \int \frac {(3+x)^3 \left (30-68 x+30 x^2-4 x^3\right )}{27-9 x-3 x^2+x^3} \, dx=-x^{4} - 6 \, x^{3} + 2 \, x^{2} + 78 \, x + \frac {432}{x - 3} \]
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Time = 0.05 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30 \[ \int \frac {(3+x)^3 \left (30-68 x+30 x^2-4 x^3\right )}{27-9 x-3 x^2+x^3} \, dx=78\,x+\frac {432}{x-3}+2\,x^2-6\,x^3-x^4 \]
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