Integrand size = 11, antiderivative size = 12 \[ \int \frac {1}{2} \left (7+2 e^x\right ) \, dx=-\frac {9}{4}+e^x+\frac {7 x}{2} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2225} \[ \int \frac {1}{2} \left (7+2 e^x\right ) \, dx=\frac {7 x}{2}+e^x \]
[In]
[Out]
Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \left (7+2 e^x\right ) \, dx \\ & = \frac {7 x}{2}+\int e^x \, dx \\ & = e^x+\frac {7 x}{2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {1}{2} \left (7+2 e^x\right ) \, dx=e^x+\frac {7 x}{2} \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.58
method | result | size |
default | \(\frac {7 x}{2}+{\mathrm e}^{x}\) | \(7\) |
norman | \(\frac {7 x}{2}+{\mathrm e}^{x}\) | \(7\) |
risch | \(\frac {7 x}{2}+{\mathrm e}^{x}\) | \(7\) |
parallelrisch | \(\frac {7 x}{2}+{\mathrm e}^{x}\) | \(7\) |
parts | \(\frac {7 x}{2}+{\mathrm e}^{x}\) | \(7\) |
derivativedivides | \({\mathrm e}^{x}+\frac {7 \ln \left ({\mathrm e}^{x}\right )}{2}\) | \(9\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.50 \[ \int \frac {1}{2} \left (7+2 e^x\right ) \, dx=\frac {7}{2} \, x + e^{x} \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.58 \[ \int \frac {1}{2} \left (7+2 e^x\right ) \, dx=\frac {7 x}{2} + e^{x} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.50 \[ \int \frac {1}{2} \left (7+2 e^x\right ) \, dx=\frac {7}{2} \, x + e^{x} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.50 \[ \int \frac {1}{2} \left (7+2 e^x\right ) \, dx=\frac {7}{2} \, x + e^{x} \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.50 \[ \int \frac {1}{2} \left (7+2 e^x\right ) \, dx=\frac {7\,x}{2}+{\mathrm {e}}^x \]
[In]
[Out]