Integrand size = 30, antiderivative size = 22 \[ \int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{e^{25} x^2} \, dx=3 \left (-e^x+\frac {4-\frac {4}{e^{25}}}{x}-11 x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 6, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 14, 2225} \[ \int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{e^{25} x^2} \, dx=-33 x-3 e^x+\frac {12 \left (1-\frac {1}{e^{25}}\right )}{x} \]
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Rule 12
Rule 14
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{x^2} \, dx}{e^{25}} \\ & = \frac {\int \left (-3 e^{25+x}-\frac {3 \left (-4+4 e^{25}+11 e^{25} x^2\right )}{x^2}\right ) \, dx}{e^{25}} \\ & = -\frac {3 \int e^{25+x} \, dx}{e^{25}}-\frac {3 \int \frac {-4+4 e^{25}+11 e^{25} x^2}{x^2} \, dx}{e^{25}} \\ & = -3 e^x-\frac {3 \int \left (11 e^{25}+\frac {4 \left (-1+e^{25}\right )}{x^2}\right ) \, dx}{e^{25}} \\ & = -3 e^x+\frac {12 \left (1-\frac {1}{e^{25}}\right )}{x}-33 x \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{e^{25} x^2} \, dx=-3 e^x+\frac {12}{x}-\frac {12}{e^{25} x}-33 x \]
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Time = 0.07 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
method | result | size |
risch | \(\frac {12-3 \,{\mathrm e}^{x} x -33 x^{2}-12 \,{\mathrm e}^{-25}}{x}\) | \(22\) |
norman | \(\frac {-33 x^{2}+12 \left ({\mathrm e}^{25}-1\right ) {\mathrm e}^{-25}-3 \,{\mathrm e}^{x} x}{x}\) | \(26\) |
parts | \(-3 \,{\mathrm e}^{-25} \left (11 x \,{\mathrm e}^{25}-\frac {4 \,{\mathrm e}^{25}-4}{x}\right )-3 \,{\mathrm e}^{x}\) | \(29\) |
default | \({\mathrm e}^{-25} \left (-\frac {12}{x}+\frac {12 \,{\mathrm e}^{25}}{x}-3 \,{\mathrm e}^{x} {\mathrm e}^{25}-33 x \,{\mathrm e}^{25}\right )\) | \(30\) |
parallelrisch | \(-\frac {{\mathrm e}^{-25} \left (33 x^{2} {\mathrm e}^{25}+3 x \,{\mathrm e}^{25} {\mathrm e}^{x}+12-12 \,{\mathrm e}^{25}\right )}{x}\) | \(30\) |
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Time = 0.26 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.14 \[ \int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{e^{25} x^2} \, dx=-\frac {3 \, {\left ({\left (11 \, x^{2} - 4\right )} e^{25} + x e^{\left (x + 25\right )} + 4\right )} e^{\left (-25\right )}}{x} \]
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Time = 0.07 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{e^{25} x^2} \, dx=\frac {- 33 x e^{25} - \frac {12 - 12 e^{25}}{x}}{e^{25}} - 3 e^{x} \]
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Time = 0.20 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{e^{25} x^2} \, dx=-3 \, {\left (11 \, x e^{25} - \frac {4 \, e^{25}}{x} + \frac {4}{x} + e^{\left (x + 25\right )}\right )} e^{\left (-25\right )} \]
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Time = 0.29 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{e^{25} x^2} \, dx=-\frac {3 \, {\left (11 \, x^{2} e^{25} + x e^{\left (x + 25\right )} - 4 \, e^{25} + 4\right )} e^{\left (-25\right )}}{x} \]
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Time = 0.10 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {12-3 e^{25+x} x^2+e^{25} \left (-12-33 x^2\right )}{e^{25} x^2} \, dx=-33\,x-3\,{\mathrm {e}}^x-\frac {12\,{\mathrm {e}}^{-25}-12}{x} \]
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