Integrand size = 17, antiderivative size = 24 \[ \int \frac {1}{25} \left (25-15 e x^2-24 x^3\right ) \, dx=x+x^2-x \left (x+\frac {1}{5} x^2 \left (e+\frac {6 x}{5}\right )\right ) \]
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Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12} \[ \int \frac {1}{25} \left (25-15 e x^2-24 x^3\right ) \, dx=-\frac {6 x^4}{25}-\frac {e x^3}{5}+x \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {1}{25} \int \left (25-15 e x^2-24 x^3\right ) \, dx \\ & = x-\frac {e x^3}{5}-\frac {6 x^4}{25} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int \frac {1}{25} \left (25-15 e x^2-24 x^3\right ) \, dx=x-\frac {e x^3}{5}-\frac {6 x^4}{25} \]
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Time = 0.20 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.62
method | result | size |
default | \(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\) | \(15\) |
norman | \(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\) | \(15\) |
risch | \(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\) | \(15\) |
parallelrisch | \(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\) | \(15\) |
parts | \(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\) | \(15\) |
gosper | \(-\frac {x \left (5 x^{2} {\mathrm e}+6 x^{3}-25\right )}{25}\) | \(18\) |
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Time = 0.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58 \[ \int \frac {1}{25} \left (25-15 e x^2-24 x^3\right ) \, dx=-\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \]
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Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.62 \[ \int \frac {1}{25} \left (25-15 e x^2-24 x^3\right ) \, dx=- \frac {6 x^{4}}{25} - \frac {e x^{3}}{5} + x \]
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none
Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58 \[ \int \frac {1}{25} \left (25-15 e x^2-24 x^3\right ) \, dx=-\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \]
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Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58 \[ \int \frac {1}{25} \left (25-15 e x^2-24 x^3\right ) \, dx=-\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \]
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Time = 0.03 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58 \[ \int \frac {1}{25} \left (25-15 e x^2-24 x^3\right ) \, dx=-\frac {6\,x^4}{25}-\frac {\mathrm {e}\,x^3}{5}+x \]
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