Optimal. Leaf size=34 \[ e^4-e^6 \left (-\frac {3}{5}-e+\frac {3}{x}\right )^2 \left (1+\left (1+e^x\right ) x\right )^2 \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(296\) vs. \(2(34)=68\).
time = 0.36, antiderivative size = 296, normalized size of antiderivative = 8.71, number of steps
used = 24, number of rules used = 9, integrand size = 183, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {12, 14, 2227,
2225, 2207, 1626, 2230, 2208, 2209} \begin {gather*} -\frac {2}{25} (3+5 e)^2 e^{x+6} x^2-\frac {1}{25} (3+5 e)^2 e^{2 x+6} x^2-\frac {1}{25} e^6 (3+5 e)^2 x^2-\frac {9 e^6}{x^2}+\frac {1}{25} \left (81+120 e-25 e^2\right ) e^{2 x+6} x+\frac {6}{25} \left (21+20 e-25 e^2\right ) e^{x+6} x+\frac {2}{25} e^6 (36+5 (9-5 e) e) x+\frac {4}{25} (3+5 e)^2 e^{x+6} x+\frac {1}{25} (3+5 e)^2 e^{2 x+6} x-\frac {3}{5} (12-5 e) e^{2 x+6}-\frac {1}{50} \left (81+120 e-25 e^2\right ) e^{2 x+6}-\frac {6}{25} \left (21+20 e-25 e^2\right ) e^{x+6}-\frac {2}{25} (54-5 (54-5 e) e) e^{x+6}-\frac {4}{25} (3+5 e)^2 e^{x+6}-\frac {1}{50} (3+5 e)^2 e^{2 x+6}-\frac {18 e^{x+6}}{x}-\frac {6 (12-5 e) e^6}{5 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 1626
Rule 2207
Rule 2208
Rule 2209
Rule 2225
Rule 2227
Rule 2230
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {e^6 \left (450+360 x+72 x^3-18 x^4+e \left (-150 x+90 x^3-60 x^4\right )+e^2 \left (-50 x^3-50 x^4\right )\right )+e^{6+x} \left (450 x-450 x^2-108 x^3+126 x^4-18 x^5+e \left (540 x^3+120 x^4-60 x^5\right )+e^2 \left (-50 x^3-150 x^4-50 x^5\right )\right )+e^{6+2 x} \left (-360 x^3+162 x^4-18 x^5+e \left (150 x^3+240 x^4-60 x^5\right )+e^2 \left (-50 x^4-50 x^5\right )\right )}{x^3} \, dx\\ &=\frac {1}{25} \int \left (2 e^{6+2 x} (15-(3+5 e) x) (-12+5 e+(3+5 e) x)+\frac {2 e^6 (1+x) (15-(3+5 e) x) \left (15+(3+5 e) x^2\right )}{x^3}+\frac {2 e^{6+x} (15-(3+5 e) x) \left (15-(12-5 e) x-3 (2-5 e) x^2+(3+5 e) x^3\right )}{x^2}\right ) \, dx\\ &=\frac {2}{25} \int e^{6+2 x} (15-(3+5 e) x) (-12+5 e+(3+5 e) x) \, dx+\frac {2}{25} \int \frac {e^{6+x} (15-(3+5 e) x) \left (15-(12-5 e) x-3 (2-5 e) x^2+(3+5 e) x^3\right )}{x^2} \, dx+\frac {1}{25} \left (2 e^6\right ) \int \frac {(1+x) (15-(3+5 e) x) \left (15+(3+5 e) x^2\right )}{x^3} \, dx\\ &=\frac {2}{25} \int \left (-54 e^{6+x} \left (1+\frac {5}{54} e (-54+5 e)\right )+\frac {225 e^{6+x}}{x^2}-\frac {225 e^{6+x}}{x}-3 e^{6+x} \left (-21-20 e+25 e^2\right ) x-e^{6+x} (3+5 e)^2 x^2\right ) \, dx+\frac {2}{25} \int \left (15 e^{6+2 x} (-12+5 e)-e^{6+2 x} \left (-81-120 e+25 e^2\right ) x-e^{6+2 x} (3+5 e)^2 x^2\right ) \, dx+\frac {1}{25} \left (2 e^6\right ) \int \left (36 \left (1-\frac {5}{36} e (-9+5 e)\right )+\frac {225}{x^3}-\frac {15 (-12+5 e)}{x^2}-(3+5 e)^2 x\right ) \, dx\\ &=-\frac {9 e^6}{x^2}-\frac {6 (12-5 e) e^6}{5 x}+\frac {2}{25} e^6 (36+5 (9-5 e) e) x-\frac {1}{25} e^6 (3+5 e)^2 x^2+18 \int \frac {e^{6+x}}{x^2} \, dx-18 \int \frac {e^{6+x}}{x} \, dx-\frac {1}{5} (6 (12-5 e)) \int e^{6+2 x} \, dx-\frac {1}{25} \left (2 (3+5 e)^2\right ) \int e^{6+x} x^2 \, dx-\frac {1}{25} \left (2 (3+5 e)^2\right ) \int e^{6+2 x} x^2 \, dx-\frac {1}{25} (2 (54-5 (54-5 e) e)) \int e^{6+x} \, dx+\frac {1}{25} \left (6 \left (21+20 e-25 e^2\right )\right ) \int e^{6+x} x \, dx+\frac {1}{25} \left (2 \left (81+120 e-25 e^2\right )\right ) \int e^{6+2 x} x \, dx\\ &=-\frac {3}{5} (12-5 e) e^{6+2 x}-\frac {2}{25} e^{6+x} (54-5 (54-5 e) e)-\frac {9 e^6}{x^2}-\frac {6 (12-5 e) e^6}{5 x}-\frac {18 e^{6+x}}{x}+\frac {2}{25} e^6 (36+5 (9-5 e) e) x+\frac {6}{25} e^{6+x} \left (21+20 e-25 e^2\right ) x+\frac {1}{25} e^{6+2 x} \left (81+120 e-25 e^2\right ) x-\frac {1}{25} e^6 (3+5 e)^2 x^2-\frac {2}{25} e^{6+x} (3+5 e)^2 x^2-\frac {1}{25} e^{6+2 x} (3+5 e)^2 x^2-18 e^6 \text {Ei}(x)+18 \int \frac {e^{6+x}}{x} \, dx+\frac {1}{25} \left (2 (3+5 e)^2\right ) \int e^{6+2 x} x \, dx+\frac {1}{25} \left (4 (3+5 e)^2\right ) \int e^{6+x} x \, dx-\frac {1}{25} \left (6 \left (21+20 e-25 e^2\right )\right ) \int e^{6+x} \, dx+\frac {1}{25} \left (-81-120 e+25 e^2\right ) \int e^{6+2 x} \, dx\\ &=-\frac {3}{5} (12-5 e) e^{6+2 x}-\frac {2}{25} e^{6+x} (54-5 (54-5 e) e)-\frac {6}{25} e^{6+x} \left (21+20 e-25 e^2\right )-\frac {1}{50} e^{6+2 x} \left (81+120 e-25 e^2\right )-\frac {9 e^6}{x^2}-\frac {6 (12-5 e) e^6}{5 x}-\frac {18 e^{6+x}}{x}+\frac {4}{25} e^{6+x} (3+5 e)^2 x+\frac {1}{25} e^{6+2 x} (3+5 e)^2 x+\frac {2}{25} e^6 (36+5 (9-5 e) e) x+\frac {6}{25} e^{6+x} \left (21+20 e-25 e^2\right ) x+\frac {1}{25} e^{6+2 x} \left (81+120 e-25 e^2\right ) x-\frac {1}{25} e^6 (3+5 e)^2 x^2-\frac {2}{25} e^{6+x} (3+5 e)^2 x^2-\frac {1}{25} e^{6+2 x} (3+5 e)^2 x^2-\frac {1}{25} (3+5 e)^2 \int e^{6+2 x} \, dx-\frac {1}{25} \left (4 (3+5 e)^2\right ) \int e^{6+x} \, dx\\ &=-\frac {3}{5} (12-5 e) e^{6+2 x}-\frac {4}{25} e^{6+x} (3+5 e)^2-\frac {1}{50} e^{6+2 x} (3+5 e)^2-\frac {2}{25} e^{6+x} (54-5 (54-5 e) e)-\frac {6}{25} e^{6+x} \left (21+20 e-25 e^2\right )-\frac {1}{50} e^{6+2 x} \left (81+120 e-25 e^2\right )-\frac {9 e^6}{x^2}-\frac {6 (12-5 e) e^6}{5 x}-\frac {18 e^{6+x}}{x}+\frac {4}{25} e^{6+x} (3+5 e)^2 x+\frac {1}{25} e^{6+2 x} (3+5 e)^2 x+\frac {2}{25} e^6 (36+5 (9-5 e) e) x+\frac {6}{25} e^{6+x} \left (21+20 e-25 e^2\right ) x+\frac {1}{25} e^{6+2 x} \left (81+120 e-25 e^2\right ) x-\frac {1}{25} e^6 (3+5 e)^2 x^2-\frac {2}{25} e^{6+x} (3+5 e)^2 x^2-\frac {1}{25} e^{6+2 x} (3+5 e)^2 x^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(86\) vs. \(2(34)=68\).
time = 1.38, size = 86, normalized size = 2.53 \begin {gather*} -\frac {e^6 \left (225+30 \left (12-5 e+15 e^x\right ) x+15 e^x \left (18-20 e+15 e^x\right ) x^2-2 (3+5 e) \left (1+e^x\right ) \left (12-5 e+15 e^x\right ) x^3+(3+5 e)^2 \left (1+e^x\right )^2 x^4\right )}{25 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.08, size = 457, normalized size = 13.44
method | result | size |
risch | \(-\frac {6 \,{\mathrm e}^{6} {\mathrm e} x^{2}}{5}+\frac {18 \,{\mathrm e}^{6} x \,{\mathrm e}}{5}-\frac {9 x^{2} {\mathrm e}^{6}}{25}+\frac {72 x \,{\mathrm e}^{6}}{25}-{\mathrm e}^{6} x^{2} {\mathrm e}^{2}-2 \,{\mathrm e}^{6} x \,{\mathrm e}^{2}+\frac {\left (150 \,{\mathrm e}^{7}-360 \,{\mathrm e}^{6}\right ) x -225 \,{\mathrm e}^{6}}{25 x^{2}}+\frac {\left (-25 x^{2} {\mathrm e}^{8}-30 x^{2} {\mathrm e}^{7}+150 x \,{\mathrm e}^{7}-9 x^{2} {\mathrm e}^{6}+90 x \,{\mathrm e}^{6}-225 \,{\mathrm e}^{6}\right ) {\mathrm e}^{2 x}}{25}-\frac {2 \left (25 x^{3} {\mathrm e}^{2}+25 x^{2} {\mathrm e}^{2}+30 x^{3} {\mathrm e}-120 x^{2} {\mathrm e}+9 x^{3}-150 x \,{\mathrm e}-81 x^{2}+135 x +225\right ) {\mathrm e}^{x +6}}{25 x}\) | \(170\) |
norman | \(\frac {\left (6 \,{\mathrm e} \,{\mathrm e}^{6}-\frac {72 \,{\mathrm e}^{6}}{5}\right ) x +\left (-2 \,{\mathrm e}^{2} {\mathrm e}^{6}+\frac {18 \,{\mathrm e} \,{\mathrm e}^{6}}{5}+\frac {72 \,{\mathrm e}^{6}}{25}\right ) x^{3}+\left (-{\mathrm e}^{2} {\mathrm e}^{6}-\frac {6 \,{\mathrm e} \,{\mathrm e}^{6}}{5}-\frac {9 \,{\mathrm e}^{6}}{25}\right ) x^{4}+\left (6 \,{\mathrm e} \,{\mathrm e}^{6}+\frac {18 \,{\mathrm e}^{6}}{5}\right ) x^{3} {\mathrm e}^{2 x}+\left (12 \,{\mathrm e} \,{\mathrm e}^{6}-\frac {54 \,{\mathrm e}^{6}}{5}\right ) x^{2} {\mathrm e}^{x}+\left (-2 \,{\mathrm e}^{2} {\mathrm e}^{6}-\frac {12 \,{\mathrm e} \,{\mathrm e}^{6}}{5}-\frac {18 \,{\mathrm e}^{6}}{25}\right ) x^{4} {\mathrm e}^{x}+\left (-2 \,{\mathrm e}^{2} {\mathrm e}^{6}+\frac {48 \,{\mathrm e} \,{\mathrm e}^{6}}{5}+\frac {162 \,{\mathrm e}^{6}}{25}\right ) x^{3} {\mathrm e}^{x}+\left (-{\mathrm e}^{2} {\mathrm e}^{6}-\frac {6 \,{\mathrm e} \,{\mathrm e}^{6}}{5}-\frac {9 \,{\mathrm e}^{6}}{25}\right ) x^{4} {\mathrm e}^{2 x}-9 \,{\mathrm e}^{6}-9 x^{2} {\mathrm e}^{6} {\mathrm e}^{2 x}-18 x \,{\mathrm e}^{6} {\mathrm e}^{x}}{x^{2}}\) | \(248\) |
default | \(-\frac {9 x^{2} {\mathrm e}^{6}}{25}+\frac {72 x \,{\mathrm e}^{6}}{25}-\frac {108 \,{\mathrm e}^{6} {\mathrm e}^{x}}{25}-\frac {72 \,{\mathrm e}^{6}}{5 x}-{\mathrm e}^{6} x^{2} {\mathrm e}^{2}-2 \,{\mathrm e}^{6} x \,{\mathrm e}^{2}-\frac {18 \,{\mathrm e}^{6} \left ({\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}\right )}{25}+\frac {162 \,{\mathrm e}^{6} \left (\frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}\right )}{25}+18 \,{\mathrm e}^{6} \expIntegral \left (1, -x \right )+18 \,{\mathrm e}^{6} \left (-\frac {{\mathrm e}^{x}}{x}-\expIntegral \left (1, -x \right )\right )-\frac {36 \,{\mathrm e}^{6} {\mathrm e}^{2 x}}{5}-\frac {9 \,{\mathrm e}^{6}}{x^{2}}+\frac {126 \,{\mathrm e}^{6} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )}{25}-\frac {18 \,{\mathrm e}^{6} \left (\frac {{\mathrm e}^{2 x} x^{2}}{2}-\frac {x \,{\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{2 x}}{4}\right )}{25}-\frac {6 \,{\mathrm e}^{6} {\mathrm e} x^{2}}{5}+\frac {18 \,{\mathrm e}^{6} x \,{\mathrm e}}{5}-2 \,{\mathrm e}^{6} {\mathrm e}^{x} {\mathrm e}^{2}+\frac {108 \,{\mathrm e}^{6} {\mathrm e}^{x} {\mathrm e}}{5}+3 \,{\mathrm e}^{6} {\mathrm e}^{2 x} {\mathrm e}+\frac {6 \,{\mathrm e} \,{\mathrm e}^{6}}{x}+\frac {24 \,{\mathrm e} \,{\mathrm e}^{6} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )}{5}-6 \,{\mathrm e}^{6} {\mathrm e}^{2} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )+\frac {48 \,{\mathrm e} \,{\mathrm e}^{6} \left (\frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}\right )}{5}-2 \,{\mathrm e}^{6} {\mathrm e}^{2} \left (\frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}\right )-\frac {12 \,{\mathrm e} \,{\mathrm e}^{6} \left ({\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}\right )}{5}-2 \,{\mathrm e}^{6} {\mathrm e}^{2} \left ({\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}\right )-\frac {12 \,{\mathrm e} \,{\mathrm e}^{6} \left (\frac {{\mathrm e}^{2 x} x^{2}}{2}-\frac {x \,{\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{2 x}}{4}\right )}{5}-2 \,{\mathrm e}^{6} {\mathrm e}^{2} \left (\frac {{\mathrm e}^{2 x} x^{2}}{2}-\frac {x \,{\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{2 x}}{4}\right )\) | \(457\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.29, size = 317, normalized size = 9.32 \begin {gather*} -x^{2} e^{8} - \frac {6}{5} \, x^{2} e^{7} - \frac {9}{25} \, x^{2} e^{6} - 2 \, x e^{8} + \frac {18}{5} \, x e^{7} + \frac {72}{25} \, x e^{6} - 18 \, {\rm Ei}\left (x\right ) e^{6} - \frac {1}{2} \, {\left (2 \, x^{2} e^{8} - 2 \, x e^{8} + e^{8}\right )} e^{\left (2 \, x\right )} - \frac {3}{5} \, {\left (2 \, x^{2} e^{7} - 2 \, x e^{7} + e^{7}\right )} e^{\left (2 \, x\right )} - \frac {9}{50} \, {\left (2 \, x^{2} e^{6} - 2 \, x e^{6} + e^{6}\right )} e^{\left (2 \, x\right )} - \frac {1}{2} \, {\left (2 \, x e^{8} - e^{8}\right )} e^{\left (2 \, x\right )} + \frac {12}{5} \, {\left (2 \, x e^{7} - e^{7}\right )} e^{\left (2 \, x\right )} + \frac {81}{50} \, {\left (2 \, x e^{6} - e^{6}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{2} e^{8} - 2 \, x e^{8} + 2 \, e^{8}\right )} e^{x} - \frac {12}{5} \, {\left (x^{2} e^{7} - 2 \, x e^{7} + 2 \, e^{7}\right )} e^{x} - \frac {18}{25} \, {\left (x^{2} e^{6} - 2 \, x e^{6} + 2 \, e^{6}\right )} e^{x} - 6 \, {\left (x e^{8} - e^{8}\right )} e^{x} + \frac {24}{5} \, {\left (x e^{7} - e^{7}\right )} e^{x} + \frac {126}{25} \, {\left (x e^{6} - e^{6}\right )} e^{x} + 18 \, e^{6} \Gamma \left (-1, -x\right ) + \frac {6 \, e^{7}}{x} - \frac {72 \, e^{6}}{5 \, x} - \frac {9 \, e^{6}}{x^{2}} + 3 \, e^{\left (2 \, x + 7\right )} - \frac {36}{5} \, e^{\left (2 \, x + 6\right )} - 2 \, e^{\left (x + 8\right )} + \frac {108}{5} \, e^{\left (x + 7\right )} - \frac {108}{25} \, e^{\left (x + 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 154 vs.
\(2 (30) = 60\).
time = 0.38, size = 154, normalized size = 4.53 \begin {gather*} -\frac {{\left (25 \, {\left (x^{4} + 2 \, x^{3}\right )} e^{14} + 30 \, {\left (x^{4} - 3 \, x^{3} - 5 \, x\right )} e^{13} + 9 \, {\left (x^{4} - 8 \, x^{3} + 40 \, x + 25\right )} e^{12} + {\left (25 \, x^{4} e^{2} + 9 \, x^{4} - 90 \, x^{3} + 225 \, x^{2} + 30 \, {\left (x^{4} - 5 \, x^{3}\right )} e\right )} e^{\left (2 \, x + 12\right )} + 2 \, {\left (25 \, {\left (x^{4} + x^{3}\right )} e^{8} + 30 \, {\left (x^{4} - 4 \, x^{3} - 5 \, x^{2}\right )} e^{7} + 9 \, {\left (x^{4} - 9 \, x^{3} + 15 \, x^{2} + 25 \, x\right )} e^{6}\right )} e^{\left (x + 6\right )}\right )} e^{\left (-6\right )}}{25 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 190 vs.
\(2 (27) = 54\).
time = 0.27, size = 190, normalized size = 5.59 \begin {gather*} - \frac {x^{2} \cdot \left (9 e^{6} + 30 e^{7} + 25 e^{8}\right )}{25} - \frac {x \left (- 90 e^{7} - 72 e^{6} + 50 e^{8}\right )}{25} + \frac {\left (- 625 x^{3} e^{8} - 750 x^{3} e^{7} - 225 x^{3} e^{6} + 2250 x^{2} e^{6} + 3750 x^{2} e^{7} - 5625 x e^{6}\right ) e^{2 x} + \left (- 1250 x^{3} e^{8} - 1500 x^{3} e^{7} - 450 x^{3} e^{6} - 1250 x^{2} e^{8} + 4050 x^{2} e^{6} + 6000 x^{2} e^{7} - 6750 x e^{6} + 7500 x e^{7} - 11250 e^{6}\right ) e^{x}}{625 x} - \frac {x \left (- 150 e^{7} + 360 e^{6}\right ) + 225 e^{6}}{25 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 453 vs.
\(2 (30) = 60\).
time = 0.40, size = 453, normalized size = 13.32 \begin {gather*} -\frac {25 \, {\left (x + 6\right )}^{4} e^{23} + 30 \, {\left (x + 6\right )}^{4} e^{22} + 9 \, {\left (x + 6\right )}^{4} e^{21} + 25 \, {\left (x + 6\right )}^{4} e^{\left (2 \, x + 23\right )} + 30 \, {\left (x + 6\right )}^{4} e^{\left (2 \, x + 22\right )} + 9 \, {\left (x + 6\right )}^{4} e^{\left (2 \, x + 21\right )} + 50 \, {\left (x + 6\right )}^{4} e^{\left (x + 23\right )} + 60 \, {\left (x + 6\right )}^{4} e^{\left (x + 22\right )} + 18 \, {\left (x + 6\right )}^{4} e^{\left (x + 21\right )} - 550 \, {\left (x + 6\right )}^{3} e^{23} - 810 \, {\left (x + 6\right )}^{3} e^{22} - 288 \, {\left (x + 6\right )}^{3} e^{21} - 600 \, {\left (x + 6\right )}^{3} e^{\left (2 \, x + 23\right )} - 870 \, {\left (x + 6\right )}^{3} e^{\left (2 \, x + 22\right )} - 306 \, {\left (x + 6\right )}^{3} e^{\left (2 \, x + 21\right )} - 1150 \, {\left (x + 6\right )}^{3} e^{\left (x + 23\right )} - 1680 \, {\left (x + 6\right )}^{3} e^{\left (x + 22\right )} - 594 \, {\left (x + 6\right )}^{3} e^{\left (x + 21\right )} + 3900 \, {\left (x + 6\right )}^{2} e^{23} + 6480 \, {\left (x + 6\right )}^{2} e^{22} + 2484 \, {\left (x + 6\right )}^{2} e^{21} + 5400 \, {\left (x + 6\right )}^{2} e^{\left (2 \, x + 23\right )} + 9180 \, {\left (x + 6\right )}^{2} e^{\left (2 \, x + 22\right )} + 3789 \, {\left (x + 6\right )}^{2} e^{\left (2 \, x + 21\right )} + 9900 \, {\left (x + 6\right )}^{2} e^{\left (x + 23\right )} + 16980 \, {\left (x + 6\right )}^{2} e^{\left (x + 22\right )} + 7074 \, {\left (x + 6\right )}^{2} e^{\left (x + 21\right )} - 9000 \, {\left (x + 6\right )} e^{23} - 16350 \, {\left (x + 6\right )} e^{22} - 6120 \, {\left (x + 6\right )} e^{21} - 21600 \, {\left (x + 6\right )} e^{\left (2 \, x + 23\right )} - 42120 \, {\left (x + 6\right )} e^{\left (2 \, x + 22\right )} - 20196 \, {\left (x + 6\right )} e^{\left (2 \, x + 21\right )} - 37800 \, {\left (x + 6\right )} e^{\left (x + 23\right )} - 74160 \, {\left (x + 6\right )} e^{\left (x + 22\right )} - 35838 \, {\left (x + 6\right )} e^{\left (x + 21\right )} + 900 \, e^{22} - 1935 \, e^{21} + 32400 \, e^{\left (2 \, x + 23\right )} + 71280 \, e^{\left (2 \, x + 22\right )} + 39204 \, e^{\left (2 \, x + 21\right )} + 54000 \, e^{\left (x + 23\right )} + 118800 \, e^{\left (x + 22\right )} + 65340 \, e^{\left (x + 21\right )}}{25 \, {\left ({\left (x + 6\right )}^{2} e^{15} - 12 \, {\left (x + 6\right )} e^{15} + 36 \, e^{15}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.87, size = 139, normalized size = 4.09 \begin {gather*} {\mathrm {e}}^{x+6}\,\left (12\,\mathrm {e}-\frac {54}{5}\right )-x^2\,\left (\frac {9\,{\mathrm {e}}^6}{25}+\frac {6\,{\mathrm {e}}^7}{5}+{\mathrm {e}}^8+{\mathrm {e}}^{2\,x+6}\,\left (\frac {6\,\mathrm {e}}{5}+{\mathrm {e}}^2+\frac {9}{25}\right )+{\mathrm {e}}^{x+6}\,\left (\frac {12\,\mathrm {e}}{5}+2\,{\mathrm {e}}^2+\frac {18}{25}\right )\right )-\frac {9\,{\mathrm {e}}^6+x\,\left (18\,{\mathrm {e}}^{x+6}+\frac {72\,{\mathrm {e}}^6}{5}-6\,{\mathrm {e}}^7\right )}{x^2}-9\,{\mathrm {e}}^{2\,x+6}+x\,\left (\frac {72\,{\mathrm {e}}^6}{25}+\frac {18\,{\mathrm {e}}^7}{5}-2\,{\mathrm {e}}^8+{\mathrm {e}}^{x+6}\,\left (\frac {48\,\mathrm {e}}{5}-2\,{\mathrm {e}}^2+\frac {162}{25}\right )+{\mathrm {e}}^{2\,x+12}\,\left (6\,{\mathrm {e}}^{-5}+\frac {18\,{\mathrm {e}}^{-6}}{5}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________