Integrand size = 23, antiderivative size = 27 \[ \int \frac {1}{144} \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx=1-e^{3+4 e^x}+\frac {1}{144} \left (-e^x-x\right )+x \]
[Out]
Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {12, 2225, 2320} \[ \int \frac {1}{144} \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx=\frac {143 x}{144}-e^{4 e^x+3}-\frac {e^x}{144} \]
[In]
[Out]
Rule 12
Rule 2225
Rule 2320
Rubi steps \begin{align*} \text {integral}& = \frac {1}{144} \int \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx \\ & = \frac {143 x}{144}-\frac {\int e^x \, dx}{144}-4 \int e^{3+4 e^x+x} \, dx \\ & = -\frac {e^x}{144}+\frac {143 x}{144}-4 \text {Subst}\left (\int e^{3+4 x} \, dx,x,e^x\right ) \\ & = -e^{3+4 e^x}-\frac {e^x}{144}+\frac {143 x}{144} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {1}{144} \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx=\frac {1}{144} \left (-144 e^{3+4 e^x}-e^x+143 x\right ) \]
[In]
[Out]
Time = 0.38 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.67
method | result | size |
default | \(\frac {143 x}{144}-{\mathrm e}^{4 \,{\mathrm e}^{x}+3}-\frac {{\mathrm e}^{x}}{144}\) | \(18\) |
norman | \(\frac {143 x}{144}-{\mathrm e}^{4 \,{\mathrm e}^{x}+3}-\frac {{\mathrm e}^{x}}{144}\) | \(18\) |
risch | \(\frac {143 x}{144}-{\mathrm e}^{4 \,{\mathrm e}^{x}+3}-\frac {{\mathrm e}^{x}}{144}\) | \(18\) |
parallelrisch | \(\frac {143 x}{144}-{\mathrm e}^{4 \,{\mathrm e}^{x}+3}-\frac {{\mathrm e}^{x}}{144}\) | \(18\) |
parts | \(\frac {143 x}{144}-{\mathrm e}^{4 \,{\mathrm e}^{x}+3}-\frac {{\mathrm e}^{x}}{144}\) | \(18\) |
derivativedivides | \(\frac {143 \ln \left (4 \,{\mathrm e}^{x}\right )}{144}-\frac {{\mathrm e}^{x}}{144}-\frac {1}{192}-{\mathrm e}^{4 \,{\mathrm e}^{x}+3}\) | \(23\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.04 \[ \int \frac {1}{144} \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx=\frac {1}{144} \, {\left (143 \, x e^{x} - e^{\left (2 \, x\right )} - 144 \, e^{\left (x + 4 \, e^{x} + 3\right )}\right )} e^{\left (-x\right )} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \frac {1}{144} \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx=\frac {143 x}{144} - \frac {e^{x}}{144} - e^{4 e^{x} + 3} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \frac {1}{144} \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx=\frac {143}{144} \, x - \frac {1}{144} \, e^{x} - e^{\left (4 \, e^{x} + 3\right )} \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \frac {1}{144} \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx=\frac {143}{144} \, x - \frac {1}{144} \, e^{x} - e^{\left (4 \, e^{x} + 3\right )} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \frac {1}{144} \left (143-e^x-576 e^{3+4 e^x+x}\right ) \, dx=\frac {143\,x}{144}-\frac {{\mathrm {e}}^x}{144}-{\mathrm {e}}^3\,{\mathrm {e}}^{4\,{\mathrm {e}}^x} \]
[In]
[Out]