Optimal. Leaf size=30 \[ -e^x+\log \left (3+5 e^{18 (-4+3 x)^2} (3-x)-x\right ) \]
________________________________________________________________________________________
Rubi [F] time = 0.69, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1+e^x (3-x)+e^{288-432 x+162 x^2} \left (6485+e^x (15-5 x)-7020 x+1620 x^2\right )}{-3+x+e^{288-432 x+162 x^2} (-15+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {108 e^{432 x} (-4+3 x)}{e^{432 x}+5 e^{288+162 x^2}}+\frac {1297+3 e^x-1404 x-e^x x+324 x^2}{-3+x}\right ) \, dx\\ &=-\left (108 \int \frac {e^{432 x} (-4+3 x)}{e^{432 x}+5 e^{288+162 x^2}} \, dx\right )+\int \frac {1297+3 e^x-1404 x-e^x x+324 x^2}{-3+x} \, dx\\ &=-\left (108 \int \left (-\frac {4 e^{432 x}}{e^{432 x}+5 e^{288+162 x^2}}+\frac {3 e^{432 x} x}{e^{432 x}+5 e^{288+162 x^2}}\right ) \, dx\right )+\int \left (-e^x+\frac {1297-1404 x+324 x^2}{-3+x}\right ) \, dx\\ &=-\left (324 \int \frac {e^{432 x} x}{e^{432 x}+5 e^{288+162 x^2}} \, dx\right )+432 \int \frac {e^{432 x}}{e^{432 x}+5 e^{288+162 x^2}} \, dx-\int e^x \, dx+\int \frac {1297-1404 x+324 x^2}{-3+x} \, dx\\ &=-e^x-324 \int \frac {e^{432 x} x}{e^{432 x}+5 e^{288+162 x^2}} \, dx+432 \int \frac {e^{432 x}}{e^{432 x}+5 e^{288+162 x^2}} \, dx+\int \left (-432+\frac {1}{-3+x}+324 x\right ) \, dx\\ &=-e^x-432 x+162 x^2+\log (3-x)-324 \int \frac {e^{432 x} x}{e^{432 x}+5 e^{288+162 x^2}} \, dx+432 \int \frac {e^{432 x}}{e^{432 x}+5 e^{288+162 x^2}} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.40, size = 29, normalized size = 0.97 \begin {gather*} -e^x+\log \left (1+5 e^{288-432 x+162 x^2}\right )+\log (3-x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.73, size = 25, normalized size = 0.83 \begin {gather*} -e^{x} + \log \left (x - 3\right ) + \log \left (5 \, e^{\left (162 \, x^{2} - 432 \, x + 288\right )} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.36, size = 29, normalized size = 0.97 \begin {gather*} -x - e^{x} + \log \left (x - 3\right ) + \log \left (5 \, e^{\left (162 \, x^{2} - 431 \, x + 288\right )} + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 24, normalized size = 0.80
method | result | size |
risch | \(\ln \left (x -3\right )-{\mathrm e}^{x}-288+\ln \left ({\mathrm e}^{18 \left (3 x -4\right )^{2}}+\frac {1}{5}\right )\) | \(24\) |
norman | \(-{\mathrm e}^{x}+\ln \left (x -3\right )+\ln \left (5 \,{\mathrm e}^{162 x^{2}-432 x +288}+1\right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.87, size = 32, normalized size = 1.07 \begin {gather*} -432 \, x - e^{x} + \log \left (\frac {1}{5} \, {\left (5 \, e^{\left (162 \, x^{2} + 288\right )} + e^{\left (432 \, x\right )}\right )} e^{\left (-288\right )}\right ) + \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.16, size = 26, normalized size = 0.87 \begin {gather*} \ln \left (\left (x-3\right )\,\left (5\,{\mathrm {e}}^{-432\,x}\,{\mathrm {e}}^{288}\,{\mathrm {e}}^{162\,x^2}+1\right )\right )-{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.23, size = 24, normalized size = 0.80 \begin {gather*} - e^{x} + \log {\left (x - 3 \right )} + \log {\left (e^{162 x^{2} - 432 x + 288} + \frac {1}{5} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________