Integrand size = 11, antiderivative size = 9 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=e^x+\frac {25 x}{24} \]
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Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2225} \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25 x}{24}+e^x \]
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Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {1}{24} \int \left (25+24 e^x\right ) \, dx \\ & = \frac {25 x}{24}+\int e^x \, dx \\ & = e^x+\frac {25 x}{24} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=e^x+\frac {25 x}{24} \]
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Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78
method | result | size |
default | \(\frac {25 x}{24}+{\mathrm e}^{x}\) | \(7\) |
norman | \(\frac {25 x}{24}+{\mathrm e}^{x}\) | \(7\) |
risch | \(\frac {25 x}{24}+{\mathrm e}^{x}\) | \(7\) |
parallelrisch | \(\frac {25 x}{24}+{\mathrm e}^{x}\) | \(7\) |
parts | \(\frac {25 x}{24}+{\mathrm e}^{x}\) | \(7\) |
derivativedivides | \({\mathrm e}^{x}+\frac {25 \ln \left ({\mathrm e}^{x}\right )}{24}\) | \(9\) |
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none
Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25}{24} \, x + e^{x} \]
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Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25 x}{24} + e^{x} \]
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none
Time = 0.20 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25}{24} \, x + e^{x} \]
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none
Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25}{24} \, x + e^{x} \]
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Time = 15.62 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25\,x}{24}+{\mathrm {e}}^x \]
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