Integrand size = 367, antiderivative size = 27 \[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx=\left (2-e^{8+\frac {3 x}{5}}+x\right )^4 \left (\frac {4}{x}+\log ^2(x)\right ) \]
[Out]
\[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx=\int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \frac {1}{5} \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{x^2} \, dx \\ & = \frac {1}{5} \int \left (\frac {10 (2+x)^3 \left (-4+6 x+2 x \log (x)+x^2 \log (x)+2 x^2 \log ^2(x)\right )}{x^2}+\frac {2 e^{32+\frac {12 x}{5}} \left (-10+24 x+5 x \log (x)+6 x^2 \log ^2(x)\right )}{x^2}+\frac {12 e^{16+\frac {6 x}{5}} (2+x) \left (-20+34 x+12 x^2+10 x \log (x)+5 x^2 \log (x)+11 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2}-\frac {4 e^{8+\frac {3 x}{5}} (2+x)^2 \left (-40+64 x+12 x^2+20 x \log (x)+10 x^2 \log (x)+21 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2}-\frac {4 e^{24+\frac {9 x}{5}} \left (-40+72 x+36 x^2+20 x \log (x)+10 x^2 \log (x)+23 x^2 \log ^2(x)+9 x^3 \log ^2(x)\right )}{x^2}\right ) \, dx \\ & = \frac {2}{5} \int \frac {e^{32+\frac {12 x}{5}} \left (-10+24 x+5 x \log (x)+6 x^2 \log ^2(x)\right )}{x^2} \, dx-\frac {4}{5} \int \frac {e^{8+\frac {3 x}{5}} (2+x)^2 \left (-40+64 x+12 x^2+20 x \log (x)+10 x^2 \log (x)+21 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2} \, dx-\frac {4}{5} \int \frac {e^{24+\frac {9 x}{5}} \left (-40+72 x+36 x^2+20 x \log (x)+10 x^2 \log (x)+23 x^2 \log ^2(x)+9 x^3 \log ^2(x)\right )}{x^2} \, dx+2 \int \frac {(2+x)^3 \left (-4+6 x+2 x \log (x)+x^2 \log (x)+2 x^2 \log ^2(x)\right )}{x^2} \, dx+\frac {12}{5} \int \frac {e^{16+\frac {6 x}{5}} (2+x) \left (-20+34 x+12 x^2+10 x \log (x)+5 x^2 \log (x)+11 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2} \, dx \\ & = \frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {4}{5} \int \left (\frac {4 e^{8+\frac {3 x}{5}} (2+x)^2 \left (-10+16 x+3 x^2\right )}{x^2}+\frac {10 e^{8+\frac {3 x}{5}} (2+x)^3 \log (x)}{x}+3 e^{8+\frac {3 x}{5}} (2+x)^2 (7+x) \log ^2(x)\right ) \, dx-\frac {4}{5} \int \left (\frac {4 e^{24+\frac {9 x}{5}} \left (-10+18 x+9 x^2\right )}{x^2}+\frac {10 e^{24+\frac {9 x}{5}} (2+x) \log (x)}{x}+e^{24+\frac {9 x}{5}} (23+9 x) \log ^2(x)\right ) \, dx+2 \int \left (\frac {2 (2+x)^3 (-2+3 x)}{x^2}+\frac {(2+x)^4 \log (x)}{x}+2 (2+x)^3 \log ^2(x)\right ) \, dx+\frac {12}{5} \int \left (\frac {2 e^{16+\frac {6 x}{5}} (2+x) \left (-10+17 x+6 x^2\right )}{x^2}+\frac {5 e^{16+\frac {6 x}{5}} (2+x)^2 \log (x)}{x}+e^{16+\frac {6 x}{5}} \left (22+17 x+3 x^2\right ) \log ^2(x)\right ) \, dx \\ & = \frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {4}{5} \int e^{24+\frac {9 x}{5}} (23+9 x) \log ^2(x) \, dx+2 \int \frac {(2+x)^4 \log (x)}{x} \, dx-\frac {12}{5} \int e^{8+\frac {3 x}{5}} (2+x)^2 (7+x) \log ^2(x) \, dx+\frac {12}{5} \int e^{16+\frac {6 x}{5}} \left (22+17 x+3 x^2\right ) \log ^2(x) \, dx-\frac {16}{5} \int \frac {e^{8+\frac {3 x}{5}} (2+x)^2 \left (-10+16 x+3 x^2\right )}{x^2} \, dx-\frac {16}{5} \int \frac {e^{24+\frac {9 x}{5}} \left (-10+18 x+9 x^2\right )}{x^2} \, dx+4 \int \frac {(2+x)^3 (-2+3 x)}{x^2} \, dx+4 \int (2+x)^3 \log ^2(x) \, dx+\frac {24}{5} \int \frac {e^{16+\frac {6 x}{5}} (2+x) \left (-10+17 x+6 x^2\right )}{x^2} \, dx-8 \int \frac {e^{24+\frac {9 x}{5}} (2+x) \log (x)}{x} \, dx-8 \int \frac {e^{8+\frac {3 x}{5}} (2+x)^3 \log (x)}{x} \, dx+12 \int \frac {e^{16+\frac {6 x}{5}} (2+x)^2 \log (x)}{x} \, dx \\ & = \frac {4 (2+x)^4}{x}-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)+64 x \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)+24 x^2 \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)+\frac {16}{3} x^3 \log (x)+\frac {1}{2} x^4 \log (x)-64 e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right ) \log (x)+48 e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right ) \log (x)-16 e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right ) \log (x)+32 \log ^2(x)+(2+x)^4 \log ^2(x)+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {4}{5} \int \left (23 e^{24+\frac {9 x}{5}} \log ^2(x)+9 e^{24+\frac {9 x}{5}} x \log ^2(x)\right ) \, dx-2 \int \frac {(2+x)^4 \log (x)}{x} \, dx-2 \int \left (32+12 x+\frac {8 x^2}{3}+\frac {x^3}{4}+\frac {16 \log (x)}{x}\right ) \, dx+\frac {12}{5} \int \left (22 e^{16+\frac {6 x}{5}} \log ^2(x)+17 e^{16+\frac {6 x}{5}} x \log ^2(x)+3 e^{16+\frac {6 x}{5}} x^2 \log ^2(x)\right ) \, dx-\frac {12}{5} \int \left (28 e^{8+\frac {3 x}{5}} \log ^2(x)+32 e^{8+\frac {3 x}{5}} x \log ^2(x)+11 e^{8+\frac {3 x}{5}} x^2 \log ^2(x)+e^{8+\frac {3 x}{5}} x^3 \log ^2(x)\right ) \, dx-\frac {16}{5} \int \left (9 e^{24+\frac {9 x}{5}}-\frac {10 e^{24+\frac {9 x}{5}}}{x^2}+\frac {18 e^{24+\frac {9 x}{5}}}{x}\right ) \, dx-\frac {16}{5} \int \left (66 e^{8+\frac {3 x}{5}}-\frac {40 e^{8+\frac {3 x}{5}}}{x^2}+\frac {24 e^{8+\frac {3 x}{5}}}{x}+28 e^{8+\frac {3 x}{5}} x+3 e^{8+\frac {3 x}{5}} x^2\right ) \, dx+\frac {24}{5} \int \left (29 e^{16+\frac {6 x}{5}}-\frac {20 e^{16+\frac {6 x}{5}}}{x^2}+\frac {24 e^{16+\frac {6 x}{5}}}{x}+6 e^{16+\frac {6 x}{5}} x\right ) \, dx+8 \int \frac {e^8 \left (5 e^{3 x/5} \left (68+24 x+9 x^2\right )+216 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )\right )}{27 x} \, dx+8 \int \frac {e^{24} \left (5 e^{9 x/5}+18 \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )\right )}{9 x} \, dx-12 \int \frac {e^{16} \left (5 e^{6 x/5} (19+6 x)+144 \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )\right )}{36 x} \, dx \\ & = -64 x-12 x^2-\frac {16 x^3}{9}-\frac {x^4}{8}+\frac {4 (2+x)^4}{x}-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)-64 e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right ) \log (x)+48 e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right ) \log (x)-16 e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right ) \log (x)+(2+x)^4 \log ^2(x)+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}+2 \int \left (32+12 x+\frac {8 x^2}{3}+\frac {x^3}{4}+\frac {16 \log (x)}{x}\right ) \, dx-\frac {12}{5} \int e^{8+\frac {3 x}{5}} x^3 \log ^2(x) \, dx-\frac {36}{5} \int e^{24+\frac {9 x}{5}} x \log ^2(x) \, dx+\frac {36}{5} \int e^{16+\frac {6 x}{5}} x^2 \log ^2(x) \, dx-\frac {48}{5} \int e^{8+\frac {3 x}{5}} x^2 \, dx-\frac {92}{5} \int e^{24+\frac {9 x}{5}} \log ^2(x) \, dx-\frac {132}{5} \int e^{8+\frac {3 x}{5}} x^2 \log ^2(x) \, dx-\frac {144}{5} \int e^{24+\frac {9 x}{5}} \, dx+\frac {144}{5} \int e^{16+\frac {6 x}{5}} x \, dx+32 \int \frac {e^{24+\frac {9 x}{5}}}{x^2} \, dx-32 \int \frac {\log (x)}{x} \, dx+\frac {204}{5} \int e^{16+\frac {6 x}{5}} x \log ^2(x) \, dx+\frac {264}{5} \int e^{16+\frac {6 x}{5}} \log ^2(x) \, dx-\frac {288}{5} \int \frac {e^{24+\frac {9 x}{5}}}{x} \, dx-\frac {336}{5} \int e^{8+\frac {3 x}{5}} \log ^2(x) \, dx-\frac {384}{5} \int \frac {e^{8+\frac {3 x}{5}}}{x} \, dx-\frac {384}{5} \int e^{8+\frac {3 x}{5}} x \log ^2(x) \, dx-\frac {448}{5} \int e^{8+\frac {3 x}{5}} x \, dx-96 \int \frac {e^{16+\frac {6 x}{5}}}{x^2} \, dx+\frac {576}{5} \int \frac {e^{16+\frac {6 x}{5}}}{x} \, dx+128 \int \frac {e^{8+\frac {3 x}{5}}}{x^2} \, dx+\frac {696}{5} \int e^{16+\frac {6 x}{5}} \, dx-\frac {1056}{5} \int e^{8+\frac {3 x}{5}} \, dx+\frac {1}{27} \left (8 e^8\right ) \int \frac {5 e^{3 x/5} \left (68+24 x+9 x^2\right )+216 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )}{x} \, dx-\frac {1}{3} e^{16} \int \frac {5 e^{6 x/5} (19+6 x)+144 \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )}{x} \, dx+\frac {1}{9} \left (8 e^{24}\right ) \int \frac {5 e^{9 x/5}+18 \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )}{x} \, dx \\ & = -352 e^{8+\frac {3 x}{5}}+116 e^{16+\frac {6 x}{5}}-16 e^{24+\frac {9 x}{5}}-\frac {128 e^{8+\frac {3 x}{5}}}{x}+\frac {96 e^{16+\frac {6 x}{5}}}{x}-\frac {32 e^{24+\frac {9 x}{5}}}{x}-\frac {448}{3} e^{8+\frac {3 x}{5}} x+24 e^{16+\frac {6 x}{5}} x-16 e^{8+\frac {3 x}{5}} x^2+\frac {4 (2+x)^4}{x}-\frac {384}{5} e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )+\frac {576}{5} e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )-\frac {288}{5} e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)-64 e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right ) \log (x)+48 e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right ) \log (x)-16 e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right ) \log (x)-16 \log ^2(x)+(2+x)^4 \log ^2(x)+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {12}{5} \int e^{8+\frac {3 x}{5}} x^3 \log ^2(x) \, dx-\frac {36}{5} \int e^{24+\frac {9 x}{5}} x \log ^2(x) \, dx+\frac {36}{5} \int e^{16+\frac {6 x}{5}} x^2 \log ^2(x) \, dx-24 \int e^{16+\frac {6 x}{5}} \, dx-\frac {132}{5} \int e^{8+\frac {3 x}{5}} x^2 \log ^2(x) \, dx+32 \int e^{8+\frac {3 x}{5}} x \, dx+32 \int \frac {\log (x)}{x} \, dx+\frac {204}{5} \int e^{16+\frac {6 x}{5}} x \log ^2(x) \, dx+\frac {288}{5} \int \frac {e^{24+\frac {9 x}{5}}}{x} \, dx+\frac {384}{5} \int \frac {e^{8+\frac {3 x}{5}}}{x} \, dx-\frac {384}{5} \int e^{8+\frac {3 x}{5}} x \log ^2(x) \, dx-92 \text {Subst}\left (\int e^{24+9 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )-\frac {576}{5} \int \frac {e^{16+\frac {6 x}{5}}}{x} \, dx+\frac {448}{3} \int e^{8+\frac {3 x}{5}} \, dx+264 \text {Subst}\left (\int e^{16+6 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )-336 \text {Subst}\left (\int e^{8+3 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+\frac {1}{27} \left (8 e^8\right ) \int \left (\frac {5 e^{3 x/5} \left (68+24 x+9 x^2\right )}{x}+\frac {216 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )}{x}\right ) \, dx-\frac {1}{3} e^{16} \int \left (\frac {5 e^{6 x/5} (19+6 x)}{x}+\frac {144 \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )}{x}\right ) \, dx+\frac {1}{9} \left (8 e^{24}\right ) \int \left (\frac {5 e^{9 x/5}}{x}+\frac {18 \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )}{x}\right ) \, dx \\ & = -\frac {928}{9} e^{8+\frac {3 x}{5}}+96 e^{16+\frac {6 x}{5}}-16 e^{24+\frac {9 x}{5}}-\frac {128 e^{8+\frac {3 x}{5}}}{x}+\frac {96 e^{16+\frac {6 x}{5}}}{x}-\frac {32 e^{24+\frac {9 x}{5}}}{x}-96 e^{8+\frac {3 x}{5}} x+24 e^{16+\frac {6 x}{5}} x-16 e^{8+\frac {3 x}{5}} x^2+\frac {4 (2+x)^4}{x}-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)-64 e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right ) \log (x)+48 e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right ) \log (x)-16 e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right ) \log (x)+(2+x)^4 \log ^2(x)+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {12}{5} \int e^{8+\frac {3 x}{5}} x^3 \log ^2(x) \, dx-\frac {36}{5} \int e^{24+\frac {9 x}{5}} x \log ^2(x) \, dx+\frac {36}{5} \int e^{16+\frac {6 x}{5}} x^2 \log ^2(x) \, dx-\frac {132}{5} \int e^{8+\frac {3 x}{5}} x^2 \log ^2(x) \, dx+\frac {204}{5} \int e^{16+\frac {6 x}{5}} x \log ^2(x) \, dx-\frac {160}{3} \int e^{8+\frac {3 x}{5}} \, dx-\frac {384}{5} \int e^{8+\frac {3 x}{5}} x \log ^2(x) \, dx-92 \text {Subst}\left (\int e^{24+9 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+264 \text {Subst}\left (\int e^{16+6 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )-336 \text {Subst}\left (\int e^{8+3 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+\frac {1}{27} \left (40 e^8\right ) \int \frac {e^{3 x/5} \left (68+24 x+9 x^2\right )}{x} \, dx+\left (64 e^8\right ) \int \frac {\operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )}{x} \, dx-\frac {1}{3} \left (5 e^{16}\right ) \int \frac {e^{6 x/5} (19+6 x)}{x} \, dx-\left (48 e^{16}\right ) \int \frac {\operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )}{x} \, dx+\frac {1}{9} \left (40 e^{24}\right ) \int \frac {e^{9 x/5}}{x} \, dx+\left (16 e^{24}\right ) \int \frac {\operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )}{x} \, dx \\ & = -192 e^{8+\frac {3 x}{5}}+96 e^{16+\frac {6 x}{5}}-16 e^{24+\frac {9 x}{5}}-\frac {128 e^{8+\frac {3 x}{5}}}{x}+\frac {96 e^{16+\frac {6 x}{5}}}{x}-\frac {32 e^{24+\frac {9 x}{5}}}{x}-96 e^{8+\frac {3 x}{5}} x+24 e^{16+\frac {6 x}{5}} x-16 e^{8+\frac {3 x}{5}} x^2+\frac {4 (2+x)^4}{x}+\frac {40}{9} e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)-64 e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right ) \log (x)+64 e^8 \left (\operatorname {ExpIntegralE}\left (1,-\frac {3 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )\right ) \log (x)+48 e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right ) \log (x)-48 e^{16} \left (\operatorname {ExpIntegralE}\left (1,-\frac {6 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )\right ) \log (x)-16 e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right ) \log (x)+16 e^{24} \left (\operatorname {ExpIntegralE}\left (1,-\frac {9 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )\right ) \log (x)+(2+x)^4 \log ^2(x)+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {12}{5} \int e^{8+\frac {3 x}{5}} x^3 \log ^2(x) \, dx-\frac {36}{5} \int e^{24+\frac {9 x}{5}} x \log ^2(x) \, dx+\frac {36}{5} \int e^{16+\frac {6 x}{5}} x^2 \log ^2(x) \, dx-\frac {132}{5} \int e^{8+\frac {3 x}{5}} x^2 \log ^2(x) \, dx+\frac {204}{5} \int e^{16+\frac {6 x}{5}} x \log ^2(x) \, dx-\frac {384}{5} \int e^{8+\frac {3 x}{5}} x \log ^2(x) \, dx-92 \text {Subst}\left (\int e^{24+9 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+264 \text {Subst}\left (\int e^{16+6 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )-336 \text {Subst}\left (\int e^{8+3 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+\frac {1}{27} \left (40 e^8\right ) \int \left (24 e^{3 x/5}+\frac {68 e^{3 x/5}}{x}+9 e^{3 x/5} x\right ) \, dx-\left (64 e^8\right ) \int \frac {\operatorname {ExpIntegralE}\left (1,-\frac {3 x}{5}\right )}{x} \, dx-\frac {1}{3} \left (5 e^{16}\right ) \int \left (6 e^{6 x/5}+\frac {19 e^{6 x/5}}{x}\right ) \, dx+\left (48 e^{16}\right ) \int \frac {\operatorname {ExpIntegralE}\left (1,-\frac {6 x}{5}\right )}{x} \, dx-\left (16 e^{24}\right ) \int \frac {\operatorname {ExpIntegralE}\left (1,-\frac {9 x}{5}\right )}{x} \, dx \\ & = -192 e^{8+\frac {3 x}{5}}+96 e^{16+\frac {6 x}{5}}-16 e^{24+\frac {9 x}{5}}-\frac {128 e^{8+\frac {3 x}{5}}}{x}+\frac {96 e^{16+\frac {6 x}{5}}}{x}-\frac {32 e^{24+\frac {9 x}{5}}}{x}-96 e^{8+\frac {3 x}{5}} x+24 e^{16+\frac {6 x}{5}} x-16 e^{8+\frac {3 x}{5}} x^2+\frac {4 (2+x)^4}{x}+\frac {40}{9} e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )+\frac {192}{5} e^8 x \, _3F_3\left (1,1,1;2,2,2;\frac {3 x}{5}\right )-\frac {288}{5} e^{16} x \, _3F_3\left (1,1,1;2,2,2;\frac {6 x}{5}\right )+\frac {144}{5} e^{24} x \, _3F_3\left (1,1,1;2,2,2;\frac {9 x}{5}\right )+8 e^{24} \log ^2\left (-\frac {9 x}{5}\right )-24 e^{16} \log ^2\left (-\frac {6 x}{5}\right )+32 e^8 \log ^2\left (-\frac {3 x}{5}\right )-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)+64 e^8 \gamma \log (x)-48 e^{16} \gamma \log (x)+16 e^{24} \gamma \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)-64 e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right ) \log (x)+64 e^8 \left (\operatorname {ExpIntegralE}\left (1,-\frac {3 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )\right ) \log (x)+48 e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right ) \log (x)-48 e^{16} \left (\operatorname {ExpIntegralE}\left (1,-\frac {6 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )\right ) \log (x)-16 e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right ) \log (x)+16 e^{24} \left (\operatorname {ExpIntegralE}\left (1,-\frac {9 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )\right ) \log (x)+(2+x)^4 \log ^2(x)+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {12}{5} \int e^{8+\frac {3 x}{5}} x^3 \log ^2(x) \, dx-\frac {36}{5} \int e^{24+\frac {9 x}{5}} x \log ^2(x) \, dx+\frac {36}{5} \int e^{16+\frac {6 x}{5}} x^2 \log ^2(x) \, dx-\frac {132}{5} \int e^{8+\frac {3 x}{5}} x^2 \log ^2(x) \, dx+\frac {204}{5} \int e^{16+\frac {6 x}{5}} x \log ^2(x) \, dx-\frac {384}{5} \int e^{8+\frac {3 x}{5}} x \log ^2(x) \, dx-92 \text {Subst}\left (\int e^{24+9 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+264 \text {Subst}\left (\int e^{16+6 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )-336 \text {Subst}\left (\int e^{8+3 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+\frac {1}{3} \left (40 e^8\right ) \int e^{3 x/5} x \, dx+\frac {1}{9} \left (320 e^8\right ) \int e^{3 x/5} \, dx+\frac {1}{27} \left (2720 e^8\right ) \int \frac {e^{3 x/5}}{x} \, dx-\left (10 e^{16}\right ) \int e^{6 x/5} \, dx-\frac {1}{3} \left (95 e^{16}\right ) \int \frac {e^{6 x/5}}{x} \, dx \\ & = -\frac {3584}{27} e^{8+\frac {3 x}{5}}+\frac {263}{3} e^{16+\frac {6 x}{5}}-16 e^{24+\frac {9 x}{5}}-\frac {128 e^{8+\frac {3 x}{5}}}{x}+\frac {96 e^{16+\frac {6 x}{5}}}{x}-\frac {32 e^{24+\frac {9 x}{5}}}{x}-\frac {664}{9} e^{8+\frac {3 x}{5}} x+24 e^{16+\frac {6 x}{5}} x-16 e^{8+\frac {3 x}{5}} x^2+\frac {4 (2+x)^4}{x}+\frac {2720}{27} e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )-\frac {95}{3} e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )+\frac {40}{9} e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )+\frac {192}{5} e^8 x \, _3F_3\left (1,1,1;2,2,2;\frac {3 x}{5}\right )-\frac {288}{5} e^{16} x \, _3F_3\left (1,1,1;2,2,2;\frac {6 x}{5}\right )+\frac {144}{5} e^{24} x \, _3F_3\left (1,1,1;2,2,2;\frac {9 x}{5}\right )+8 e^{24} \log ^2\left (-\frac {9 x}{5}\right )-24 e^{16} \log ^2\left (-\frac {6 x}{5}\right )+32 e^8 \log ^2\left (-\frac {3 x}{5}\right )-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)+64 e^8 \gamma \log (x)-48 e^{16} \gamma \log (x)+16 e^{24} \gamma \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)-64 e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right ) \log (x)+64 e^8 \left (\operatorname {ExpIntegralE}\left (1,-\frac {3 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )\right ) \log (x)+48 e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right ) \log (x)-48 e^{16} \left (\operatorname {ExpIntegralE}\left (1,-\frac {6 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )\right ) \log (x)-16 e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right ) \log (x)+16 e^{24} \left (\operatorname {ExpIntegralE}\left (1,-\frac {9 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )\right ) \log (x)+(2+x)^4 \log ^2(x)+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {12}{5} \int e^{8+\frac {3 x}{5}} x^3 \log ^2(x) \, dx-\frac {36}{5} \int e^{24+\frac {9 x}{5}} x \log ^2(x) \, dx+\frac {36}{5} \int e^{16+\frac {6 x}{5}} x^2 \log ^2(x) \, dx-\frac {132}{5} \int e^{8+\frac {3 x}{5}} x^2 \log ^2(x) \, dx+\frac {204}{5} \int e^{16+\frac {6 x}{5}} x \log ^2(x) \, dx-\frac {384}{5} \int e^{8+\frac {3 x}{5}} x \log ^2(x) \, dx-92 \text {Subst}\left (\int e^{24+9 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+264 \text {Subst}\left (\int e^{16+6 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )-336 \text {Subst}\left (\int e^{8+3 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )-\frac {1}{9} \left (200 e^8\right ) \int e^{3 x/5} \, dx \\ & = -\frac {1528}{9} e^{8+\frac {3 x}{5}}+\frac {263}{3} e^{16+\frac {6 x}{5}}-16 e^{24+\frac {9 x}{5}}-\frac {128 e^{8+\frac {3 x}{5}}}{x}+\frac {96 e^{16+\frac {6 x}{5}}}{x}-\frac {32 e^{24+\frac {9 x}{5}}}{x}-\frac {664}{9} e^{8+\frac {3 x}{5}} x+24 e^{16+\frac {6 x}{5}} x-16 e^{8+\frac {3 x}{5}} x^2+\frac {4 (2+x)^4}{x}+\frac {2720}{27} e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )-\frac {95}{3} e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )+\frac {40}{9} e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )+\frac {192}{5} e^8 x \, _3F_3\left (1,1,1;2,2,2;\frac {3 x}{5}\right )-\frac {288}{5} e^{16} x \, _3F_3\left (1,1,1;2,2,2;\frac {6 x}{5}\right )+\frac {144}{5} e^{24} x \, _3F_3\left (1,1,1;2,2,2;\frac {9 x}{5}\right )+8 e^{24} \log ^2\left (-\frac {9 x}{5}\right )-24 e^{16} \log ^2\left (-\frac {6 x}{5}\right )+32 e^8 \log ^2\left (-\frac {3 x}{5}\right )-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)+64 e^8 \gamma \log (x)-48 e^{16} \gamma \log (x)+16 e^{24} \gamma \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)-64 e^8 \operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right ) \log (x)+64 e^8 \left (\operatorname {ExpIntegralE}\left (1,-\frac {3 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {3 x}{5}\right )\right ) \log (x)+48 e^{16} \operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right ) \log (x)-48 e^{16} \left (\operatorname {ExpIntegralE}\left (1,-\frac {6 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {6 x}{5}\right )\right ) \log (x)-16 e^{24} \operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right ) \log (x)+16 e^{24} \left (\operatorname {ExpIntegralE}\left (1,-\frac {9 x}{5}\right )+\operatorname {ExpIntegralEi}\left (\frac {9 x}{5}\right )\right ) \log (x)+(2+x)^4 \log ^2(x)+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {12}{5} \int e^{8+\frac {3 x}{5}} x^3 \log ^2(x) \, dx-\frac {36}{5} \int e^{24+\frac {9 x}{5}} x \log ^2(x) \, dx+\frac {36}{5} \int e^{16+\frac {6 x}{5}} x^2 \log ^2(x) \, dx-\frac {132}{5} \int e^{8+\frac {3 x}{5}} x^2 \log ^2(x) \, dx+\frac {204}{5} \int e^{16+\frac {6 x}{5}} x \log ^2(x) \, dx-\frac {384}{5} \int e^{8+\frac {3 x}{5}} x \log ^2(x) \, dx-92 \text {Subst}\left (\int e^{24+9 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )+264 \text {Subst}\left (\int e^{16+6 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right )-336 \text {Subst}\left (\int e^{8+3 x} \log ^2(5 x) \, dx,x,\frac {x}{5}\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(104\) vs. \(2(27)=54\).
Time = 0.23 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.85 \[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx=\frac {2}{5} \left (\frac {10 \left (16+e^{32+\frac {12 x}{5}}+24 x^2+8 x^3+x^4-4 e^{24+\frac {9 x}{5}} (2+x)+6 e^{16+\frac {6 x}{5}} (2+x)^2-4 e^{8+\frac {3 x}{5}} (2+x)^3\right )}{x}+\frac {5}{2} \left (2-e^{8+\frac {3 x}{5}}+x\right )^4 \log ^2(x)\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(229\) vs. \(2(24)=48\).
Time = 0.28 (sec) , antiderivative size = 230, normalized size of antiderivative = 8.52
method | result | size |
risch | \(\frac {\left (5 x^{4}-20 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{3}+30 \,{\mathrm e}^{\frac {6 x}{5}+16} x^{2}-20 \,{\mathrm e}^{\frac {9 x}{5}+24} x +5 \,{\mathrm e}^{\frac {12 x}{5}+32}+40 x^{3}-120 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{2}+120 \,{\mathrm e}^{\frac {6 x}{5}+16} x -40 \,{\mathrm e}^{\frac {9 x}{5}+24}+120 x^{2}-240 \,{\mathrm e}^{\frac {3 x}{5}+8} x +120 \,{\mathrm e}^{\frac {6 x}{5}+16}+160 x -160 \,{\mathrm e}^{\frac {3 x}{5}+8}+80\right ) \ln \left (x \right )^{2}}{5}+\frac {4 x^{4}-16 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{3}+24 \,{\mathrm e}^{\frac {6 x}{5}+16} x^{2}-16 \,{\mathrm e}^{\frac {9 x}{5}+24} x +4 \,{\mathrm e}^{\frac {12 x}{5}+32}+32 x^{3}-96 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{2}+96 \,{\mathrm e}^{\frac {6 x}{5}+16} x -32 \,{\mathrm e}^{\frac {9 x}{5}+24}+96 x^{2}-192 \,{\mathrm e}^{\frac {3 x}{5}+8} x +96 \,{\mathrm e}^{\frac {6 x}{5}+16}-128 \,{\mathrm e}^{\frac {3 x}{5}+8}+64}{x}\) | \(230\) |
parallelrisch | \(\frac {320+40 x^{4} \ln \left (x \right )^{2}+80 x \ln \left (x \right )^{2}-640 \,{\mathrm e}^{\frac {3 x}{5}+8}+5 x^{5} \ln \left (x \right )^{2}+120 x^{3} \ln \left (x \right )^{2}+160 x^{2} \ln \left (x \right )^{2}+20 x^{4}+160 x^{3}+480 x^{2}+5 \ln \left (x \right )^{2} {\mathrm e}^{\frac {12 x}{5}+32} x -240 \ln \left (x \right )^{2} {\mathrm e}^{\frac {3 x}{5}+8} x^{2}-120 \ln \left (x \right )^{2} {\mathrm e}^{\frac {3 x}{5}+8} x^{3}-20 \ln \left (x \right )^{2} {\mathrm e}^{\frac {3 x}{5}+8} x^{4}-160 \,{\mathrm e}^{\frac {9 x}{5}+24}+30 \ln \left (x \right )^{2} {\mathrm e}^{\frac {6 x}{5}+16} x^{3}-20 \ln \left (x \right )^{2} {\mathrm e}^{\frac {9 x}{5}+24} x^{2}+120 \ln \left (x \right )^{2} {\mathrm e}^{\frac {6 x}{5}+16} x^{2}-80 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{3}-480 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{2}-960 \,{\mathrm e}^{\frac {3 x}{5}+8} x +20 \,{\mathrm e}^{\frac {12 x}{5}+32}-80 \,{\mathrm e}^{\frac {9 x}{5}+24} x +480 \,{\mathrm e}^{\frac {6 x}{5}+16} x -40 \ln \left (x \right )^{2} {\mathrm e}^{\frac {9 x}{5}+24} x +120 \ln \left (x \right )^{2} {\mathrm e}^{\frac {6 x}{5}+16} x -160 \ln \left (x \right )^{2} {\mathrm e}^{\frac {3 x}{5}+8} x +120 \,{\mathrm e}^{\frac {6 x}{5}+16} x^{2}+480 \,{\mathrm e}^{\frac {6 x}{5}+16}}{5 x}\) | \(324\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 172 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 172, normalized size of antiderivative = 6.37 \[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx=\frac {4 \, x^{4} + 32 \, x^{3} + {\left (x^{5} + 8 \, x^{4} + 24 \, x^{3} + 32 \, x^{2} + x e^{\left (\frac {12}{5} \, x + 32\right )} - 4 \, {\left (x^{2} + 2 \, x\right )} e^{\left (\frac {9}{5} \, x + 24\right )} + 6 \, {\left (x^{3} + 4 \, x^{2} + 4 \, x\right )} e^{\left (\frac {6}{5} \, x + 16\right )} - 4 \, {\left (x^{4} + 6 \, x^{3} + 12 \, x^{2} + 8 \, x\right )} e^{\left (\frac {3}{5} \, x + 8\right )} + 16 \, x\right )} \log \left (x\right )^{2} + 96 \, x^{2} - 16 \, {\left (x + 2\right )} e^{\left (\frac {9}{5} \, x + 24\right )} + 24 \, {\left (x^{2} + 4 \, x + 4\right )} e^{\left (\frac {6}{5} \, x + 16\right )} - 16 \, {\left (x^{3} + 6 \, x^{2} + 12 \, x + 8\right )} e^{\left (\frac {3}{5} \, x + 8\right )} + 4 \, e^{\left (\frac {12}{5} \, x + 32\right )} + 64}{x} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 231 vs. \(2 (20) = 40\).
Time = 0.34 (sec) , antiderivative size = 231, normalized size of antiderivative = 8.56 \[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx=4 x^{3} + 32 x^{2} + 96 x + \left (x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16\right ) \log {\left (x \right )}^{2} + \frac {64}{x} + \frac {\left (x^{4} \log {\left (x \right )}^{2} + 4 x^{3}\right ) e^{\frac {12 x}{5} + 32} + \left (- 4 x^{5} \log {\left (x \right )}^{2} - 8 x^{4} \log {\left (x \right )}^{2} - 16 x^{4} - 32 x^{3}\right ) e^{\frac {9 x}{5} + 24} + \left (6 x^{6} \log {\left (x \right )}^{2} + 24 x^{5} \log {\left (x \right )}^{2} + 24 x^{5} + 24 x^{4} \log {\left (x \right )}^{2} + 96 x^{4} + 96 x^{3}\right ) e^{\frac {6 x}{5} + 16} + \left (- 4 x^{7} \log {\left (x \right )}^{2} - 24 x^{6} \log {\left (x \right )}^{2} - 16 x^{6} - 48 x^{5} \log {\left (x \right )}^{2} - 96 x^{5} - 32 x^{4} \log {\left (x \right )}^{2} - 192 x^{4} - 128 x^{3}\right ) e^{\frac {3 x}{5} + 8}}{x^{4}} \]
[In]
[Out]
\[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx=\int { \frac {2 \, {\left (30 \, x^{4} + 160 \, x^{3} + 2 \, {\left (5 \, x^{5} + 30 \, x^{4} + 60 \, x^{3} + 3 \, x^{2} e^{\left (\frac {12}{5} \, x + 32\right )} + 40 \, x^{2} - {\left (9 \, x^{3} + 23 \, x^{2}\right )} e^{\left (\frac {9}{5} \, x + 24\right )} + 3 \, {\left (3 \, x^{4} + 17 \, x^{3} + 22 \, x^{2}\right )} e^{\left (\frac {6}{5} \, x + 16\right )} - 3 \, {\left (x^{5} + 11 \, x^{4} + 32 \, x^{3} + 28 \, x^{2}\right )} e^{\left (\frac {3}{5} \, x + 8\right )}\right )} \log \left (x\right )^{2} + 240 \, x^{2} + 2 \, {\left (12 \, x - 5\right )} e^{\left (\frac {12}{5} \, x + 32\right )} - 8 \, {\left (9 \, x^{2} + 18 \, x - 10\right )} e^{\left (\frac {9}{5} \, x + 24\right )} + 12 \, {\left (6 \, x^{3} + 29 \, x^{2} + 24 \, x - 20\right )} e^{\left (\frac {6}{5} \, x + 16\right )} - 8 \, {\left (3 \, x^{4} + 28 \, x^{3} + 66 \, x^{2} + 24 \, x - 40\right )} e^{\left (\frac {3}{5} \, x + 8\right )} + 5 \, {\left (x^{5} + 8 \, x^{4} + 24 \, x^{3} + 32 \, x^{2} + x e^{\left (\frac {12}{5} \, x + 32\right )} - 4 \, {\left (x^{2} + 2 \, x\right )} e^{\left (\frac {9}{5} \, x + 24\right )} + 6 \, {\left (x^{3} + 4 \, x^{2} + 4 \, x\right )} e^{\left (\frac {6}{5} \, x + 16\right )} - 4 \, {\left (x^{4} + 6 \, x^{3} + 12 \, x^{2} + 8 \, x\right )} e^{\left (\frac {3}{5} \, x + 8\right )} + 16 \, x\right )} \log \left (x\right ) - 160\right )}}{5 \, x^{2}} \,d x } \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 717 vs. \(2 (24) = 48\).
Time = 0.32 (sec) , antiderivative size = 717, normalized size of antiderivative = 26.56 \[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx=\text {Too large to display} \]
[In]
[Out]
Timed out. \[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx=\int \frac {\frac {{\mathrm {e}}^{\frac {12\,x}{5}+32}\,\left (48\,x-20\right )}{5}-\frac {{\mathrm {e}}^{\frac {9\,x}{5}+24}\,\left (144\,x^2+288\,x-160\right )}{5}+\frac {{\mathrm {e}}^{\frac {6\,x}{5}+16}\,\left (144\,x^3+696\,x^2+576\,x-480\right )}{5}+\frac {\ln \left (x\right )\,\left (160\,x-{\mathrm {e}}^{\frac {9\,x}{5}+24}\,\left (40\,x^2+80\,x\right )+10\,x\,{\mathrm {e}}^{\frac {12\,x}{5}+32}+{\mathrm {e}}^{\frac {6\,x}{5}+16}\,\left (60\,x^3+240\,x^2+240\,x\right )-{\mathrm {e}}^{\frac {3\,x}{5}+8}\,\left (40\,x^4+240\,x^3+480\,x^2+320\,x\right )+320\,x^2+240\,x^3+80\,x^4+10\,x^5\right )}{5}+\frac {{\ln \left (x\right )}^2\,\left (12\,x^2\,{\mathrm {e}}^{\frac {12\,x}{5}+32}-{\mathrm {e}}^{\frac {9\,x}{5}+24}\,\left (36\,x^3+92\,x^2\right )-{\mathrm {e}}^{\frac {3\,x}{5}+8}\,\left (12\,x^5+132\,x^4+384\,x^3+336\,x^2\right )+160\,x^2+240\,x^3+120\,x^4+20\,x^5+{\mathrm {e}}^{\frac {6\,x}{5}+16}\,\left (36\,x^4+204\,x^3+264\,x^2\right )\right )}{5}-\frac {{\mathrm {e}}^{\frac {3\,x}{5}+8}\,\left (48\,x^4+448\,x^3+1056\,x^2+384\,x-640\right )}{5}+96\,x^2+64\,x^3+12\,x^4-64}{x^2} \,d x \]
[In]
[Out]