Optimal. Leaf size=23 \[ \left (11+e^5+\frac {1}{3} \left (1+e^{1+\frac {23 x}{5}}\right )+x\right )^2 \]
________________________________________________________________________________________
Rubi [B] time = 0.05, antiderivative size = 71, normalized size of antiderivative = 3.09, number of steps used = 5, number of rules used = 3, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {12, 2194, 2176} \begin {gather*} x^2+\frac {2}{3} \left (34+3 e^5\right ) x-\frac {10}{69} e^{\frac {1}{5} (23 x+5)}+\frac {1}{9} e^{\frac {2}{5} (23 x+5)}+\frac {2}{207} e^{\frac {1}{5} (23 x+5)} \left (69 x+69 e^5+797\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{45} \int \left (1020+90 e^5+46 e^{\frac {2}{5} (5+23 x)}+90 x+e^{\frac {1}{5} (5+23 x)} \left (1594+138 e^5+138 x\right )\right ) \, dx\\ &=\frac {2}{3} \left (34+3 e^5\right ) x+x^2+\frac {1}{45} \int e^{\frac {1}{5} (5+23 x)} \left (1594+138 e^5+138 x\right ) \, dx+\frac {46}{45} \int e^{\frac {2}{5} (5+23 x)} \, dx\\ &=\frac {1}{9} e^{\frac {2}{5} (5+23 x)}+\frac {2}{3} \left (34+3 e^5\right ) x+x^2+\frac {2}{207} e^{\frac {1}{5} (5+23 x)} \left (797+69 e^5+69 x\right )-\frac {2}{3} \int e^{\frac {1}{5} (5+23 x)} \, dx\\ &=-\frac {10}{69} e^{\frac {1}{5} (5+23 x)}+\frac {1}{9} e^{\frac {2}{5} (5+23 x)}+\frac {2}{3} \left (34+3 e^5\right ) x+x^2+\frac {2}{207} e^{\frac {1}{5} (5+23 x)} \left (797+69 e^5+69 x\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 25, normalized size = 1.09 \begin {gather*} \frac {1}{9} \left (34+3 e^5+e^{1+\frac {23 x}{5}}+3 x\right )^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.78, size = 37, normalized size = 1.61 \begin {gather*} x^{2} + 2 \, x e^{5} + \frac {2}{9} \, {\left (3 \, x + 3 \, e^{5} + 34\right )} e^{\left (\frac {23}{5} \, x + 1\right )} + \frac {68}{3} \, x + \frac {1}{9} \, e^{\left (\frac {46}{5} \, x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.23, size = 41, normalized size = 1.78 \begin {gather*} x^{2} + 2 \, x e^{5} + \frac {2}{9} \, {\left (3 \, x + 34\right )} e^{\left (\frac {23}{5} \, x + 1\right )} + \frac {68}{3} \, x + \frac {1}{9} \, e^{\left (\frac {46}{5} \, x + 2\right )} + \frac {2}{3} \, e^{\left (\frac {23}{5} \, x + 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.05, size = 38, normalized size = 1.65
method | result | size |
risch | \(\frac {{\mathrm e}^{\frac {46 x}{5}+2}}{9}+\frac {\left (30 \,{\mathrm e}^{5}+340+30 x \right ) {\mathrm e}^{\frac {23 x}{5}+1}}{45}+2 x \,{\mathrm e}^{5}+x^{2}+\frac {68 x}{3}\) | \(38\) |
norman | \(x^{2}+\left (\frac {68}{9}+\frac {2 \,{\mathrm e}^{5}}{3}\right ) {\mathrm e}^{\frac {23 x}{5}+1}+\left (2 \,{\mathrm e}^{5}+\frac {68}{3}\right ) x +\frac {{\mathrm e}^{\frac {46 x}{5}+2}}{9}+\frac {2 \,{\mathrm e}^{\frac {23 x}{5}+1} x}{3}\) | \(45\) |
default | \(\frac {68 x}{3}+x^{2}+\frac {{\mathrm e}^{\frac {46 x}{5}+2}}{9}+\frac {10 \,{\mathrm e}^{\frac {23 x}{5}+1} \left (\frac {23 x}{5}+1\right )}{69}+\frac {1534 \,{\mathrm e}^{\frac {23 x}{5}+1}}{207}+\frac {2 \,{\mathrm e}^{\frac {23 x}{5}+1} {\mathrm e}^{5}}{3}+2 x \,{\mathrm e}^{5}\) | \(54\) |
derivativedivides | \(\frac {1534 x}{69}+\frac {7670}{1587}+\frac {25 \left (\frac {23 x}{5}+1\right )^{2}}{529}+\frac {{\mathrm e}^{\frac {46 x}{5}+2}}{9}+\frac {10 \,{\mathrm e}^{\frac {23 x}{5}+1} \left (\frac {23 x}{5}+1\right )}{69}+\frac {1534 \,{\mathrm e}^{\frac {23 x}{5}+1}}{207}+\frac {2 \,{\mathrm e}^{\frac {23 x}{5}+1} {\mathrm e}^{5}}{3}+\frac {10 \,{\mathrm e}^{5} \left (\frac {23 x}{5}+1\right )}{23}\) | \(65\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.38, size = 40, normalized size = 1.74 \begin {gather*} x^{2} + 2 \, x e^{5} + \frac {2}{9} \, {\left (3 \, x e + 3 \, e^{6} + 34 \, e\right )} e^{\left (\frac {23}{5} \, x\right )} + \frac {68}{3} \, x + \frac {1}{9} \, e^{\left (\frac {46}{5} \, x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.08, size = 27, normalized size = 1.17 \begin {gather*} \frac {\left (3\,x+{\mathrm {e}}^{\frac {23\,x}{5}+1}\right )\,\left (3\,x+6\,{\mathrm {e}}^5+{\mathrm {e}}^{\frac {23\,x}{5}+1}+68\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.14, size = 42, normalized size = 1.83 \begin {gather*} x^{2} + x \left (\frac {68}{3} + 2 e^{5}\right ) + \frac {\left (54 x + 612 + 54 e^{5}\right ) e^{\frac {23 x}{5} + 1}}{81} + \frac {e^{\frac {46 x}{5} + 2}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________