3.80.69 \(\int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} (160-288 x-144 x^2)+e^{\frac {2}{5} (40+3 x)} (-480+576 x+696 x^2+144 x^3)+e^{\frac {1}{5} (40+3 x)} (640-384 x-1056 x^2-448 x^3-48 x^4)+(160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} (-80 x-40 x^2)+e^{\frac {2}{5} (40+3 x)} (240 x+240 x^2+60 x^3)+e^{\frac {1}{5} (40+3 x)} (-320 x-480 x^2-240 x^3-40 x^4)) \log (x)+(160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} (-92 x^2-36 x^3)+e^{\frac {2}{5} (40+3 x)} (264 x^2+204 x^3+36 x^4)+e^{\frac {1}{5} (40+3 x)} (-336 x^2-384 x^3-132 x^4-12 x^5)) \log ^2(x)}{5 x^2} \, dx\)

Optimal. Leaf size=27 \[ \left (2-e^{8+\frac {3 x}{5}}+x\right )^4 \left (\frac {4}{x}+\log ^2(x)\right ) \]

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Rubi [F]  time = 4.68, 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 {-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 \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-320 + 480*x^2 + 320*x^3 + 60*x^4 + E^((4*(40 + 3*x))/5)*(-20 + 48*x) + E^((3*(40 + 3*x))/5)*(160 - 288*x
- 144*x^2) + E^((2*(40 + 3*x))/5)*(-480 + 576*x + 696*x^2 + 144*x^3) + E^((40 + 3*x)/5)*(640 - 384*x - 1056*x
^2 - 448*x^3 - 48*x^4) + (160*x + 10*E^((4*(40 + 3*x))/5)*x + 320*x^2 + 240*x^3 + 80*x^4 + 10*x^5 + E^((3*(40
+ 3*x))/5)*(-80*x - 40*x^2) + E^((2*(40 + 3*x))/5)*(240*x + 240*x^2 + 60*x^3) + E^((40 + 3*x)/5)*(-320*x - 480
*x^2 - 240*x^3 - 40*x^4))*Log[x] + (160*x^2 + 12*E^((4*(40 + 3*x))/5)*x^2 + 240*x^3 + 120*x^4 + 20*x^5 + E^((3
*(40 + 3*x))/5)*(-92*x^2 - 36*x^3) + E^((2*(40 + 3*x))/5)*(264*x^2 + 204*x^3 + 36*x^4) + E^((40 + 3*x)/5)*(-33
6*x^2 - 384*x^3 - 132*x^4 - 12*x^5))*Log[x]^2)/(5*x^2),x]

[Out]

(-1528*E^(8 + (3*x)/5))/9 + (263*E^(16 + (6*x)/5))/3 - 16*E^(24 + (9*x)/5) - (128*E^(8 + (3*x)/5))/x + (96*E^(
16 + (6*x)/5))/x - (32*E^(24 + (9*x)/5))/x - (664*E^(8 + (3*x)/5)*x)/9 + 24*E^(16 + (6*x)/5)*x - 16*E^(8 + (3*
x)/5)*x^2 + (4*(2 + x)^4)/x + (2720*E^8*ExpIntegralEi[(3*x)/5])/27 - (95*E^16*ExpIntegralEi[(6*x)/5])/3 + (40*
E^24*ExpIntegralEi[(9*x)/5])/9 + (192*E^8*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, (3*x)/5])/5 - (288*E^16*x*
HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, (6*x)/5])/5 + (144*E^24*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, (9*x
)/5])/5 + 8*E^24*Log[(-9*x)/5]^2 - 24*E^16*Log[(-6*x)/5]^2 + 32*E^8*Log[(-3*x)/5]^2 - (2720*E^(8 + (3*x)/5)*Lo
g[x])/27 + (95*E^(16 + (6*x)/5)*Log[x])/3 - (40*E^(24 + (9*x)/5)*Log[x])/9 + 64*E^8*EulerGamma*Log[x] - 48*E^1
6*EulerGamma*Log[x] + 16*E^24*EulerGamma*Log[x] - (320*E^(8 + (3*x)/5)*x*Log[x])/9 + 10*E^(16 + (6*x)/5)*x*Log
[x] - (40*E^(8 + (3*x)/5)*x^2*Log[x])/3 - 64*E^8*ExpIntegralEi[(3*x)/5]*Log[x] + 64*E^8*(ExpIntegralE[1, (-3*x
)/5] + ExpIntegralEi[(3*x)/5])*Log[x] + 48*E^16*ExpIntegralEi[(6*x)/5]*Log[x] - 48*E^16*(ExpIntegralE[1, (-6*x
)/5] + ExpIntegralEi[(6*x)/5])*Log[x] - 16*E^24*ExpIntegralEi[(9*x)/5]*Log[x] + 16*E^24*(ExpIntegralE[1, (-9*x
)/5] + ExpIntegralEi[(9*x)/5])*Log[x] + (2 + x)^4*Log[x]^2 + (E^(32 + (12*x)/5)*(4*x + x^2*Log[x]^2))/x^2 - (3
84*Defer[Int][E^(8 + (3*x)/5)*x*Log[x]^2, x])/5 + (204*Defer[Int][E^(16 + (6*x)/5)*x*Log[x]^2, x])/5 - (36*Def
er[Int][E^(24 + (9*x)/5)*x*Log[x]^2, x])/5 - (132*Defer[Int][E^(8 + (3*x)/5)*x^2*Log[x]^2, x])/5 + (36*Defer[I
nt][E^(16 + (6*x)/5)*x^2*Log[x]^2, x])/5 - (12*Defer[Int][E^(8 + (3*x)/5)*x^3*Log[x]^2, x])/5 - 336*Defer[Subs
t][Defer[Int][E^(8 + 3*x)*Log[5*x]^2, x], x, x/5] + 264*Defer[Subst][Defer[Int][E^(16 + 6*x)*Log[5*x]^2, x], x
, x/5] - 92*Defer[Subst][Defer[Int][E^(24 + 9*x)*Log[5*x]^2, x], x, x/5]

Rubi steps

\begin {gather*} \begin {aligned} \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)-\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 \text {Ei}\left (\frac {3 x}{5}\right ) \log (x)+48 e^{16} \text {Ei}\left (\frac {6 x}{5}\right ) \log (x)-16 e^{24} \text {Ei}\left (\frac {9 x}{5}\right ) \log (x)+(2+x)^4 \log ^2(x)+\frac {1}{6} \log (x) \left (384 x+144 x^2+32 x^3+3 x^4+192 \log (x)\right )+\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 \text {Ei}\left (\frac {3 x}{5}\right )\right )}{27 x} \, dx+8 \int \frac {e^{24} \left (5 e^{9 x/5}+18 \text {Ei}\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 \text {Ei}\left (\frac {6 x}{5}\right )\right )}{36 x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.24, size = 104, normalized size = 3.85 \begin {gather*} \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 ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-320 + 480*x^2 + 320*x^3 + 60*x^4 + E^((4*(40 + 3*x))/5)*(-20 + 48*x) + E^((3*(40 + 3*x))/5)*(160 -
288*x - 144*x^2) + E^((2*(40 + 3*x))/5)*(-480 + 576*x + 696*x^2 + 144*x^3) + E^((40 + 3*x)/5)*(640 - 384*x -
1056*x^2 - 448*x^3 - 48*x^4) + (160*x + 10*E^((4*(40 + 3*x))/5)*x + 320*x^2 + 240*x^3 + 80*x^4 + 10*x^5 + E^((
3*(40 + 3*x))/5)*(-80*x - 40*x^2) + E^((2*(40 + 3*x))/5)*(240*x + 240*x^2 + 60*x^3) + E^((40 + 3*x)/5)*(-320*x
- 480*x^2 - 240*x^3 - 40*x^4))*Log[x] + (160*x^2 + 12*E^((4*(40 + 3*x))/5)*x^2 + 240*x^3 + 120*x^4 + 20*x^5 +
E^((3*(40 + 3*x))/5)*(-92*x^2 - 36*x^3) + E^((2*(40 + 3*x))/5)*(264*x^2 + 204*x^3 + 36*x^4) + E^((40 + 3*x)/5
)*(-336*x^2 - 384*x^3 - 132*x^4 - 12*x^5))*Log[x]^2)/(5*x^2),x]

[Out]

(2*((10*(16 + E^(32 + (12*x)/5) + 24*x^2 + 8*x^3 + x^4 - 4*E^(24 + (9*x)/5)*(2 + x) + 6*E^(16 + (6*x)/5)*(2 +
x)^2 - 4*E^(8 + (3*x)/5)*(2 + x)^3))/x + (5*(2 - E^(8 + (3*x)/5) + x)^4*Log[x]^2)/2))/5

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fricas [B]  time = 0.63, size = 172, normalized size = 6.37 \begin {gather*} \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 \relax (x)^{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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*((12*x^2*exp(3/5*x+8)^4+(-36*x^3-92*x^2)*exp(3/5*x+8)^3+(36*x^4+204*x^3+264*x^2)*exp(3/5*x+8)^2+
(-12*x^5-132*x^4-384*x^3-336*x^2)*exp(3/5*x+8)+20*x^5+120*x^4+240*x^3+160*x^2)*log(x)^2+(10*x*exp(3/5*x+8)^4+(
-40*x^2-80*x)*exp(3/5*x+8)^3+(60*x^3+240*x^2+240*x)*exp(3/5*x+8)^2+(-40*x^4-240*x^3-480*x^2-320*x)*exp(3/5*x+8
)+10*x^5+80*x^4+240*x^3+320*x^2+160*x)*log(x)+(48*x-20)*exp(3/5*x+8)^4+(-144*x^2-288*x+160)*exp(3/5*x+8)^3+(14
4*x^3+696*x^2+576*x-480)*exp(3/5*x+8)^2+(-48*x^4-448*x^3-1056*x^2-384*x+640)*exp(3/5*x+8)+60*x^4+320*x^3+480*x
^2-320)/x^2,x, algorithm="fricas")

[Out]

(4*x^4 + 32*x^3 + (x^5 + 8*x^4 + 24*x^3 + 32*x^2 + x*e^(12/5*x + 32) - 4*(x^2 + 2*x)*e^(9/5*x + 24) + 6*(x^3 +
4*x^2 + 4*x)*e^(6/5*x + 16) - 4*(x^4 + 6*x^3 + 12*x^2 + 8*x)*e^(3/5*x + 8) + 16*x)*log(x)^2 + 96*x^2 - 16*(x
+ 2)*e^(9/5*x + 24) + 24*(x^2 + 4*x + 4)*e^(6/5*x + 16) - 16*(x^3 + 6*x^2 + 12*x + 8)*e^(3/5*x + 8) + 4*e^(12/
5*x + 32) + 64)/x

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*((12*x^2*exp(3/5*x+8)^4+(-36*x^3-92*x^2)*exp(3/5*x+8)^3+(36*x^4+204*x^3+264*x^2)*exp(3/5*x+8)^2+
(-12*x^5-132*x^4-384*x^3-336*x^2)*exp(3/5*x+8)+20*x^5+120*x^4+240*x^3+160*x^2)*log(x)^2+(10*x*exp(3/5*x+8)^4+(
-40*x^2-80*x)*exp(3/5*x+8)^3+(60*x^3+240*x^2+240*x)*exp(3/5*x+8)^2+(-40*x^4-240*x^3-480*x^2-320*x)*exp(3/5*x+8
)+10*x^5+80*x^4+240*x^3+320*x^2+160*x)*log(x)+(48*x-20)*exp(3/5*x+8)^4+(-144*x^2-288*x+160)*exp(3/5*x+8)^3+(14
4*x^3+696*x^2+576*x-480)*exp(3/5*x+8)^2+(-48*x^4-448*x^3-1056*x^2-384*x+640)*exp(3/5*x+8)+60*x^4+320*x^3+480*x
^2-320)/x^2,x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.12, size = 230, normalized size = 8.52

method	result	size
risch	\(\frac {\left (5 x^{4}-20 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{3}+30 \,{\mathrm e}^{\frac {6 x}{5}+16} x^{2}-20 \,{\mathrm e}^{\frac {9 x}{5}+24} x +5 \,{\mathrm e}^{\frac {12 x}{5}+32}+40 x^{3}-120 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{2}+120 \,{\mathrm e}^{\frac {6 x}{5}+16} x -40 \,{\mathrm e}^{\frac {9 x}{5}+24}+120 x^{2}-240 \,{\mathrm e}^{\frac {3 x}{5}+8} x +120 \,{\mathrm e}^{\frac {6 x}{5}+16}+160 x -160 \,{\mathrm e}^{\frac {3 x}{5}+8}+80\right ) \ln \relax (x )^{2}}{5}+\frac {4 x^{4}-16 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{3}+24 \,{\mathrm e}^{\frac {6 x}{5}+16} x^{2}-16 \,{\mathrm e}^{\frac {9 x}{5}+24} x +4 \,{\mathrm e}^{\frac {12 x}{5}+32}+32 x^{3}-96 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{2}+96 \,{\mathrm e}^{\frac {6 x}{5}+16} x -32 \,{\mathrm e}^{\frac {9 x}{5}+24}+96 x^{2}-192 \,{\mathrm e}^{\frac {3 x}{5}+8} x +96 \,{\mathrm e}^{\frac {6 x}{5}+16}-128 \,{\mathrm e}^{\frac {3 x}{5}+8}+64}{x}\)	\(230\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/5*((12*x^2*exp(3/5*x+8)^4+(-36*x^3-92*x^2)*exp(3/5*x+8)^3+(36*x^4+204*x^3+264*x^2)*exp(3/5*x+8)^2+(-12*x
^5-132*x^4-384*x^3-336*x^2)*exp(3/5*x+8)+20*x^5+120*x^4+240*x^3+160*x^2)*ln(x)^2+(10*x*exp(3/5*x+8)^4+(-40*x^2
-80*x)*exp(3/5*x+8)^3+(60*x^3+240*x^2+240*x)*exp(3/5*x+8)^2+(-40*x^4-240*x^3-480*x^2-320*x)*exp(3/5*x+8)+10*x^
5+80*x^4+240*x^3+320*x^2+160*x)*ln(x)+(48*x-20)*exp(3/5*x+8)^4+(-144*x^2-288*x+160)*exp(3/5*x+8)^3+(144*x^3+69
6*x^2+576*x-480)*exp(3/5*x+8)^2+(-48*x^4-448*x^3-1056*x^2-384*x+640)*exp(3/5*x+8)+60*x^4+320*x^3+480*x^2-320)/
x^2,x,method=_RETURNVERBOSE)

[Out]

1/5*(5*x^4-20*exp(3/5*x+8)*x^3+30*exp(6/5*x+16)*x^2-20*exp(9/5*x+24)*x+5*exp(12/5*x+32)+40*x^3-120*exp(3/5*x+8
)*x^2+120*exp(6/5*x+16)*x-40*exp(9/5*x+24)+120*x^2-240*exp(3/5*x+8)*x+120*exp(6/5*x+16)+160*x-160*exp(3/5*x+8)
+80)*ln(x)^2+4*(x^4-4*exp(3/5*x+8)*x^3+6*exp(6/5*x+16)*x^2-4*exp(9/5*x+24)*x+exp(12/5*x+32)+8*x^3-24*exp(3/5*x
+8)*x^2+24*exp(6/5*x+16)*x-8*exp(9/5*x+24)+24*x^2-48*exp(3/5*x+8)*x+24*exp(6/5*x+16)-32*exp(3/5*x+8)+16)/x

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{2} \, x^{4} \log \relax (x) + \frac {16}{3} \, x^{3} \log \relax (x) - 4 \, {\left (x e^{24} + 2 \, e^{24}\right )} e^{\left (\frac {9}{5} \, x\right )} \log \relax (x)^{2} + 6 \, {\left (x^{2} e^{16} + 4 \, x e^{16} + 4 \, e^{16}\right )} e^{\left (\frac {6}{5} \, x\right )} \log \relax (x)^{2} + 4 \, x^{3} + 24 \, x^{2} \log \relax (x) + {\left (x^{4} + 8 \, x^{3} + 24 \, x^{2} + 32 \, x\right )} \log \relax (x)^{2} + e^{\left (\frac {12}{5} \, x + 32\right )} \log \relax (x)^{2} + 32 \, x^{2} + \frac {48}{5} \, {\rm Ei}\left (\frac {12}{5} \, x\right ) e^{32} - \frac {288}{5} \, {\rm Ei}\left (\frac {9}{5} \, x\right ) e^{24} + \frac {576}{5} \, {\rm Ei}\left (\frac {6}{5} \, x\right ) e^{16} + \frac {416}{5} \, {\rm Ei}\left (\frac {3}{5} \, x\right ) e^{8} + 4 \, {\left (6 \, x e^{16} - 5 \, e^{16}\right )} e^{\left (\frac {6}{5} \, x\right )} - \frac {16}{9} \, {\left (9 \, x^{2} e^{8} - 30 \, x e^{8} + 50 \, e^{8}\right )} e^{\left (\frac {3}{5} \, x\right )} - 4 \, {\left ({\left (x^{3} e^{8} + 6 \, x^{2} e^{8} + 12 \, x e^{8} + 8 \, e^{8}\right )} \log \relax (x)^{2} - 40 \, e^{8} \log \relax (x)\right )} e^{\left (\frac {3}{5} \, x\right )} - \frac {448}{9} \, {\left (3 \, x e^{8} - 5 \, e^{8}\right )} e^{\left (\frac {3}{5} \, x\right )} + \frac {384}{5} \, e^{8} \Gamma \left (-1, -\frac {3}{5} \, x\right ) - \frac {576}{5} \, e^{16} \Gamma \left (-1, -\frac {6}{5} \, x\right ) + \frac {288}{5} \, e^{24} \Gamma \left (-1, -\frac {9}{5} \, x\right ) - \frac {48}{5} \, e^{32} \Gamma \left (-1, -\frac {12}{5} \, x\right ) - \frac {1}{6} \, {\left (3 \, x^{4} + 32 \, x^{3} + 144 \, x^{2} + 384 \, x\right )} \log \relax (x) + 64 \, x \log \relax (x) - 160 \, e^{\left (\frac {3}{5} \, x + 8\right )} \log \relax (x) + 16 \, \log \relax (x)^{2} + 96 \, x + \frac {64}{x} - 16 \, e^{\left (\frac {9}{5} \, x + 24\right )} + 116 \, e^{\left (\frac {6}{5} \, x + 16\right )} - 352 \, e^{\left (\frac {3}{5} \, x + 8\right )} - 160 \, \int \frac {e^{\left (\frac {3}{5} \, x + 8\right )}}{x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*((12*x^2*exp(3/5*x+8)^4+(-36*x^3-92*x^2)*exp(3/5*x+8)^3+(36*x^4+204*x^3+264*x^2)*exp(3/5*x+8)^2+
(-12*x^5-132*x^4-384*x^3-336*x^2)*exp(3/5*x+8)+20*x^5+120*x^4+240*x^3+160*x^2)*log(x)^2+(10*x*exp(3/5*x+8)^4+(
-40*x^2-80*x)*exp(3/5*x+8)^3+(60*x^3+240*x^2+240*x)*exp(3/5*x+8)^2+(-40*x^4-240*x^3-480*x^2-320*x)*exp(3/5*x+8
)+10*x^5+80*x^4+240*x^3+320*x^2+160*x)*log(x)+(48*x-20)*exp(3/5*x+8)^4+(-144*x^2-288*x+160)*exp(3/5*x+8)^3+(14
4*x^3+696*x^2+576*x-480)*exp(3/5*x+8)^2+(-48*x^4-448*x^3-1056*x^2-384*x+640)*exp(3/5*x+8)+60*x^4+320*x^3+480*x
^2-320)/x^2,x, algorithm="maxima")

[Out]

1/2*x^4*log(x) + 16/3*x^3*log(x) - 4*(x*e^24 + 2*e^24)*e^(9/5*x)*log(x)^2 + 6*(x^2*e^16 + 4*x*e^16 + 4*e^16)*e
^(6/5*x)*log(x)^2 + 4*x^3 + 24*x^2*log(x) + (x^4 + 8*x^3 + 24*x^2 + 32*x)*log(x)^2 + e^(12/5*x + 32)*log(x)^2
+ 32*x^2 + 48/5*Ei(12/5*x)*e^32 - 288/5*Ei(9/5*x)*e^24 + 576/5*Ei(6/5*x)*e^16 + 416/5*Ei(3/5*x)*e^8 + 4*(6*x*e
^16 - 5*e^16)*e^(6/5*x) - 16/9*(9*x^2*e^8 - 30*x*e^8 + 50*e^8)*e^(3/5*x) - 4*((x^3*e^8 + 6*x^2*e^8 + 12*x*e^8
+ 8*e^8)*log(x)^2 - 40*e^8*log(x))*e^(3/5*x) - 448/9*(3*x*e^8 - 5*e^8)*e^(3/5*x) + 384/5*e^8*gamma(-1, -3/5*x)
- 576/5*e^16*gamma(-1, -6/5*x) + 288/5*e^24*gamma(-1, -9/5*x) - 48/5*e^32*gamma(-1, -12/5*x) - 1/6*(3*x^4 + 3
2*x^3 + 144*x^2 + 384*x)*log(x) + 64*x*log(x) - 160*e^(3/5*x + 8)*log(x) + 16*log(x)^2 + 96*x + 64/x - 16*e^(9
/5*x + 24) + 116*e^(6/5*x + 16) - 352*e^(3/5*x + 8) - 160*integrate(e^(3/5*x + 8)/x, x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \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 \relax (x)\,\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 \relax (x)}^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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((exp((12*x)/5 + 32)*(48*x - 20))/5 - (exp((9*x)/5 + 24)*(288*x + 144*x^2 - 160))/5 + (exp((6*x)/5 + 16)*(
576*x + 696*x^2 + 144*x^3 - 480))/5 + (log(x)*(160*x - exp((9*x)/5 + 24)*(80*x + 40*x^2) + 10*x*exp((12*x)/5 +
32) + exp((6*x)/5 + 16)*(240*x + 240*x^2 + 60*x^3) - exp((3*x)/5 + 8)*(320*x + 480*x^2 + 240*x^3 + 40*x^4) +
320*x^2 + 240*x^3 + 80*x^4 + 10*x^5))/5 + (log(x)^2*(12*x^2*exp((12*x)/5 + 32) - exp((9*x)/5 + 24)*(92*x^2 + 3
6*x^3) - exp((3*x)/5 + 8)*(336*x^2 + 384*x^3 + 132*x^4 + 12*x^5) + 160*x^2 + 240*x^3 + 120*x^4 + 20*x^5 + exp(
(6*x)/5 + 16)*(264*x^2 + 204*x^3 + 36*x^4)))/5 - (exp((3*x)/5 + 8)*(384*x + 1056*x^2 + 448*x^3 + 48*x^4 - 640)
)/5 + 96*x^2 + 64*x^3 + 12*x^4 - 64)/x^2,x)

[Out]

int(((exp((12*x)/5 + 32)*(48*x - 20))/5 - (exp((9*x)/5 + 24)*(288*x + 144*x^2 - 160))/5 + (exp((6*x)/5 + 16)*(
576*x + 696*x^2 + 144*x^3 - 480))/5 + (log(x)*(160*x - exp((9*x)/5 + 24)*(80*x + 40*x^2) + 10*x*exp((12*x)/5 +
32) + exp((6*x)/5 + 16)*(240*x + 240*x^2 + 60*x^3) - exp((3*x)/5 + 8)*(320*x + 480*x^2 + 240*x^3 + 40*x^4) +
320*x^2 + 240*x^3 + 80*x^4 + 10*x^5))/5 + (log(x)^2*(12*x^2*exp((12*x)/5 + 32) - exp((9*x)/5 + 24)*(92*x^2 + 3
6*x^3) - exp((3*x)/5 + 8)*(336*x^2 + 384*x^3 + 132*x^4 + 12*x^5) + 160*x^2 + 240*x^3 + 120*x^4 + 20*x^5 + exp(
(6*x)/5 + 16)*(264*x^2 + 204*x^3 + 36*x^4)))/5 - (exp((3*x)/5 + 8)*(384*x + 1056*x^2 + 448*x^3 + 48*x^4 - 640)
)/5 + 96*x^2 + 64*x^3 + 12*x^4 - 64)/x^2, x)

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sympy [B]  time = 0.81, size = 231, normalized size = 8.56 \begin {gather*} 4 x^{3} + 32 x^{2} + 96 x + \left (x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16\right ) \log {\relax (x )}^{2} + \frac {64}{x} + \frac {\left (x^{4} \log {\relax (x )}^{2} + 4 x^{3}\right ) e^{\frac {12 x}{5} + 32} + \left (- 4 x^{5} \log {\relax (x )}^{2} - 8 x^{4} \log {\relax (x )}^{2} - 16 x^{4} - 32 x^{3}\right ) e^{\frac {9 x}{5} + 24} + \left (6 x^{6} \log {\relax (x )}^{2} + 24 x^{5} \log {\relax (x )}^{2} + 24 x^{5} + 24 x^{4} \log {\relax (x )}^{2} + 96 x^{4} + 96 x^{3}\right ) e^{\frac {6 x}{5} + 16} + \left (- 4 x^{7} \log {\relax (x )}^{2} - 24 x^{6} \log {\relax (x )}^{2} - 16 x^{6} - 48 x^{5} \log {\relax (x )}^{2} - 96 x^{5} - 32 x^{4} \log {\relax (x )}^{2} - 192 x^{4} - 128 x^{3}\right ) e^{\frac {3 x}{5} + 8}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*((12*x**2*exp(3/5*x+8)**4+(-36*x**3-92*x**2)*exp(3/5*x+8)**3+(36*x**4+204*x**3+264*x**2)*exp(3/5
*x+8)**2+(-12*x**5-132*x**4-384*x**3-336*x**2)*exp(3/5*x+8)+20*x**5+120*x**4+240*x**3+160*x**2)*ln(x)**2+(10*x
*exp(3/5*x+8)**4+(-40*x**2-80*x)*exp(3/5*x+8)**3+(60*x**3+240*x**2+240*x)*exp(3/5*x+8)**2+(-40*x**4-240*x**3-4
80*x**2-320*x)*exp(3/5*x+8)+10*x**5+80*x**4+240*x**3+320*x**2+160*x)*ln(x)+(48*x-20)*exp(3/5*x+8)**4+(-144*x**
2-288*x+160)*exp(3/5*x+8)**3+(144*x**3+696*x**2+576*x-480)*exp(3/5*x+8)**2+(-48*x**4-448*x**3-1056*x**2-384*x+
640)*exp(3/5*x+8)+60*x**4+320*x**3+480*x**2-320)/x**2,x)

[Out]

4*x**3 + 32*x**2 + 96*x + (x**4 + 8*x**3 + 24*x**2 + 32*x + 16)*log(x)**2 + 64/x + ((x**4*log(x)**2 + 4*x**3)*
exp(12*x/5 + 32) + (-4*x**5*log(x)**2 - 8*x**4*log(x)**2 - 16*x**4 - 32*x**3)*exp(9*x/5 + 24) + (6*x**6*log(x)
**2 + 24*x**5*log(x)**2 + 24*x**5 + 24*x**4*log(x)**2 + 96*x**4 + 96*x**3)*exp(6*x/5 + 16) + (-4*x**7*log(x)**
2 - 24*x**6*log(x)**2 - 16*x**6 - 48*x**5*log(x)**2 - 96*x**5 - 32*x**4*log(x)**2 - 192*x**4 - 128*x**3)*exp(3
*x/5 + 8))/x**4

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