3.58.50 \(\int \frac {-400-100 x-800 x^2+1240 x^3-816 x^4+774 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} (-16 x+4 x^2)+e^{3 x} (-32 x-56 x^2+64 x^3-12 x^4)+e^{2 x} (-40-170 x-152 x^2+144 x^3+72 x^4-72 x^5+12 x^6)+e^x (-480 x+120 x^2-204 x^3+696 x^4-448 x^5+72 x^6+16 x^7-4 x^8)+(-400+100 x-1600 x^2+2560 x^3-1968 x^4+2272 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} (-48 x+12 x^2)+e^{3 x} (-96 x-168 x^2+192 x^3-36 x^4)+e^{2 x} (-80-320 x-496 x^2+432 x^3+216 x^4-216 x^5+36 x^6)+e^x (-960 x+320 x^2-832 x^3+2128 x^4-1344 x^5+216 x^6+48 x^7-12 x^8)) \log (-4+x)+(-800 x^2+1320 x^3-1408 x^4+2202 x^5-2208 x^6+1104 x^7-264 x^8+24 x^9+e^{4 x} (-48 x+12 x^2)+e^{3 x} (-96 x-168 x^2+192 x^3-36 x^4)+e^{2 x} (-40-150 x-536 x^2+432 x^3+216 x^4-216 x^5+36 x^6)+e^x (-480 x+200 x^2-1012 x^3+2168 x^4-1344 x^5+216 x^6+48 x^7-12 x^8)) \log ^2(-4+x)+(-256 x^4+704 x^5-736 x^6+368 x^7-88 x^8+8 x^9+e^{4 x} (-16 x+4 x^2)+e^{3 x} (-32 x-56 x^2+64 x^3-12 x^4)+e^{2 x} (-192 x^2+144 x^3+72 x^4-72 x^5+12 x^6)+e^x (-384 x^3+736 x^4-448 x^5+72 x^6+16 x^7-4 x^8)) \log ^3(-4+x)+(-200-150 x-320 x^2+520 x^3-240 x^4+30 x^5+e^{2 x} (-90 x+20 x^2)+e^x (-160 x+100 x^3-20 x^4)+(-200+50 x-640 x^2+1080 x^3-520 x^4+70 x^5+e^{2 x} (-170 x+40 x^2)+e^x (-320 x+40 x^2+180 x^3-40 x^4)) \log (-4+x)+(-320 x^2+560 x^3-280 x^4+40 x^5+e^{2 x} (-80 x+20 x^2)+e^x (-160 x+40 x^2+80 x^3-20 x^4)) \log ^2(-4+x)) \log (x)-50 x \log ^2(x)}{-100 x+25 x^2+(-300 x+75 x^2) \log (-4+x)+(-300 x+75 x^2) \log ^2(-4+x)+(-100 x+25 x^2) \log ^3(-4+x)} \, dx\)

Optimal. Leaf size=34 \[ \left (\frac {1}{5} \left (e^x+2 x-x^2\right )^2+\frac {2+\log (x)}{1+\log (-4+x)}\right )^2 \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-400 - 100*x - 800*x^2 + 1240*x^3 - 816*x^4 + 774*x^5 - 736*x^6 + 368*x^7 - 88*x^8 + 8*x^9 + E^(4*x)*(-16
*x + 4*x^2) + E^(3*x)*(-32*x - 56*x^2 + 64*x^3 - 12*x^4) + E^(2*x)*(-40 - 170*x - 152*x^2 + 144*x^3 + 72*x^4 -
72*x^5 + 12*x^6) + E^x*(-480*x + 120*x^2 - 204*x^3 + 696*x^4 - 448*x^5 + 72*x^6 + 16*x^7 - 4*x^8) + (-400 + 1
00*x - 1600*x^2 + 2560*x^3 - 1968*x^4 + 2272*x^5 - 2208*x^6 + 1104*x^7 - 264*x^8 + 24*x^9 + E^(4*x)*(-48*x + 1
2*x^2) + E^(3*x)*(-96*x - 168*x^2 + 192*x^3 - 36*x^4) + E^(2*x)*(-80 - 320*x - 496*x^2 + 432*x^3 + 216*x^4 - 2
16*x^5 + 36*x^6) + E^x*(-960*x + 320*x^2 - 832*x^3 + 2128*x^4 - 1344*x^5 + 216*x^6 + 48*x^7 - 12*x^8))*Log[-4
+ x] + (-800*x^2 + 1320*x^3 - 1408*x^4 + 2202*x^5 - 2208*x^6 + 1104*x^7 - 264*x^8 + 24*x^9 + E^(4*x)*(-48*x +
12*x^2) + E^(3*x)*(-96*x - 168*x^2 + 192*x^3 - 36*x^4) + E^(2*x)*(-40 - 150*x - 536*x^2 + 432*x^3 + 216*x^4 -
216*x^5 + 36*x^6) + E^x*(-480*x + 200*x^2 - 1012*x^3 + 2168*x^4 - 1344*x^5 + 216*x^6 + 48*x^7 - 12*x^8))*Log[-
4 + x]^2 + (-256*x^4 + 704*x^5 - 736*x^6 + 368*x^7 - 88*x^8 + 8*x^9 + E^(4*x)*(-16*x + 4*x^2) + E^(3*x)*(-32*x
- 56*x^2 + 64*x^3 - 12*x^4) + E^(2*x)*(-192*x^2 + 144*x^3 + 72*x^4 - 72*x^5 + 12*x^6) + E^x*(-384*x^3 + 736*x
^4 - 448*x^5 + 72*x^6 + 16*x^7 - 4*x^8))*Log[-4 + x]^3 + (-200 - 150*x - 320*x^2 + 520*x^3 - 240*x^4 + 30*x^5
+ E^(2*x)*(-90*x + 20*x^2) + E^x*(-160*x + 100*x^3 - 20*x^4) + (-200 + 50*x - 640*x^2 + 1080*x^3 - 520*x^4 + 7
0*x^5 + E^(2*x)*(-170*x + 40*x^2) + E^x*(-320*x + 40*x^2 + 180*x^3 - 40*x^4))*Log[-4 + x] + (-320*x^2 + 560*x^
3 - 280*x^4 + 40*x^5 + E^(2*x)*(-80*x + 20*x^2) + E^x*(-160*x + 40*x^2 + 80*x^3 - 20*x^4))*Log[-4 + x]^2)*Log[
x] - 50*x*Log[x]^2)/(-100*x + 25*x^2 + (-300*x + 75*x^2)*Log[-4 + x] + (-300*x + 75*x^2)*Log[-4 + x]^2 + (-100
*x + 25*x^2)*Log[-4 + x]^3),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 1.06, size = 69, normalized size = 2.03 \begin {gather*} \frac {\left (10+e^{2 x}+4 e^x x+4 x^2-2 e^x x^2-4 x^3+x^4+\left (e^x-(-2+x) x\right )^2 \log (-4+x)+5 \log (x)\right )^2}{25 (1+\log (-4+x))^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-400 - 100*x - 800*x^2 + 1240*x^3 - 816*x^4 + 774*x^5 - 736*x^6 + 368*x^7 - 88*x^8 + 8*x^9 + E^(4*x
)*(-16*x + 4*x^2) + E^(3*x)*(-32*x - 56*x^2 + 64*x^3 - 12*x^4) + E^(2*x)*(-40 - 170*x - 152*x^2 + 144*x^3 + 72
*x^4 - 72*x^5 + 12*x^6) + E^x*(-480*x + 120*x^2 - 204*x^3 + 696*x^4 - 448*x^5 + 72*x^6 + 16*x^7 - 4*x^8) + (-4
00 + 100*x - 1600*x^2 + 2560*x^3 - 1968*x^4 + 2272*x^5 - 2208*x^6 + 1104*x^7 - 264*x^8 + 24*x^9 + E^(4*x)*(-48
*x + 12*x^2) + E^(3*x)*(-96*x - 168*x^2 + 192*x^3 - 36*x^4) + E^(2*x)*(-80 - 320*x - 496*x^2 + 432*x^3 + 216*x
^4 - 216*x^5 + 36*x^6) + E^x*(-960*x + 320*x^2 - 832*x^3 + 2128*x^4 - 1344*x^5 + 216*x^6 + 48*x^7 - 12*x^8))*L
og[-4 + x] + (-800*x^2 + 1320*x^3 - 1408*x^4 + 2202*x^5 - 2208*x^6 + 1104*x^7 - 264*x^8 + 24*x^9 + E^(4*x)*(-4
8*x + 12*x^2) + E^(3*x)*(-96*x - 168*x^2 + 192*x^3 - 36*x^4) + E^(2*x)*(-40 - 150*x - 536*x^2 + 432*x^3 + 216*
x^4 - 216*x^5 + 36*x^6) + E^x*(-480*x + 200*x^2 - 1012*x^3 + 2168*x^4 - 1344*x^5 + 216*x^6 + 48*x^7 - 12*x^8))
*Log[-4 + x]^2 + (-256*x^4 + 704*x^5 - 736*x^6 + 368*x^7 - 88*x^8 + 8*x^9 + E^(4*x)*(-16*x + 4*x^2) + E^(3*x)*
(-32*x - 56*x^2 + 64*x^3 - 12*x^4) + E^(2*x)*(-192*x^2 + 144*x^3 + 72*x^4 - 72*x^5 + 12*x^6) + E^x*(-384*x^3 +
736*x^4 - 448*x^5 + 72*x^6 + 16*x^7 - 4*x^8))*Log[-4 + x]^3 + (-200 - 150*x - 320*x^2 + 520*x^3 - 240*x^4 + 3
0*x^5 + E^(2*x)*(-90*x + 20*x^2) + E^x*(-160*x + 100*x^3 - 20*x^4) + (-200 + 50*x - 640*x^2 + 1080*x^3 - 520*x
^4 + 70*x^5 + E^(2*x)*(-170*x + 40*x^2) + E^x*(-320*x + 40*x^2 + 180*x^3 - 40*x^4))*Log[-4 + x] + (-320*x^2 +
560*x^3 - 280*x^4 + 40*x^5 + E^(2*x)*(-80*x + 20*x^2) + E^x*(-160*x + 40*x^2 + 80*x^3 - 20*x^4))*Log[-4 + x]^2
)*Log[x] - 50*x*Log[x]^2)/(-100*x + 25*x^2 + (-300*x + 75*x^2)*Log[-4 + x] + (-300*x + 75*x^2)*Log[-4 + x]^2 +
(-100*x + 25*x^2)*Log[-4 + x]^3),x]

[Out]

(10 + E^(2*x) + 4*E^x*x + 4*x^2 - 2*E^x*x^2 - 4*x^3 + x^4 + (E^x - (-2 + x)*x)^2*Log[-4 + x] + 5*Log[x])^2/(25
*(1 + Log[-4 + x])^2)

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fricas [B]  time = 0.72, size = 400, normalized size = 11.76 \begin {gather*} \frac {x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 36 \, x^{4} - 80 \, x^{3} + {\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 16 \, x^{4} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3}\right )} e^{x} + e^{\left (4 \, x\right )}\right )} \log \left (x - 4\right )^{2} + 80 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (3 \, x^{4} - 12 \, x^{3} + 12 \, x^{2} + 10\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3} + 10 \, x^{2} - 20 \, x\right )} e^{x} + 2 \, {\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 26 \, x^{4} - 40 \, x^{3} + 40 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (3 \, x^{4} - 12 \, x^{3} + 12 \, x^{2} + 5\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3} + 5 \, x^{2} - 10 \, x\right )} e^{x} + e^{\left (4 \, x\right )}\right )} \log \left (x - 4\right ) + 10 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2} - 2 \, {\left (x^{2} - 2 \, x\right )} e^{x} + {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2} - 2 \, {\left (x^{2} - 2 \, x\right )} e^{x} + e^{\left (2 \, x\right )}\right )} \log \left (x - 4\right ) + e^{\left (2 \, x\right )} + 10\right )} \log \relax (x) + 25 \, \log \relax (x)^{2} + e^{\left (4 \, x\right )} + 100}{25 \, {\left (\log \left (x - 4\right )^{2} + 2 \, \log \left (x - 4\right ) + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-50*x*log(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2-160*x)*exp(x)+40*x^5-280*x^4+560*x^3
-320*x^2)*log(x-4)^2+((40*x^2-170*x)*exp(x)^2+(-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-64
0*x^2+50*x-200)*log(x-4)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*exp(x)+30*x^5-240*x^4+520*x^3-320*x^2-
150*x-200)*log(x)+((4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-1
92*x^2)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9-88*x^8+368*x^7-736*x^6+704*x^5-25
6*x^4)*log(x-4)^3+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*
x^3-536*x^2-150*x-40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012*x^3+200*x^2-480*x)*exp(x)+24*x^9
-264*x^8+1104*x^7-2208*x^6+2202*x^5-1408*x^4+1320*x^3-800*x^2)*log(x-4)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192
*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)*exp(x)^2+(-12*x^8+48*x^7+216*x^6
-1344*x^5+2128*x^4-832*x^3+320*x^2-960*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1
600*x^2+100*x-400)*log(x-4)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+
144*x^3-152*x^2-170*x-40)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-8
8*x^8+368*x^7-736*x^6+774*x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x)*log(x-4)^3+(75*x^2-300*x)*lo
g(x-4)^2+(75*x^2-300*x)*log(x-4)+25*x^2-100*x),x, algorithm="fricas")

[Out]

1/25*(x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 36*x^4 - 80*x^3 + (x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 16*x^4 - 4*(x^2 - 2*x
)*e^(3*x) + 6*(x^4 - 4*x^3 + 4*x^2)*e^(2*x) - 4*(x^6 - 6*x^5 + 12*x^4 - 8*x^3)*e^x + e^(4*x))*log(x - 4)^2 + 8
0*x^2 - 4*(x^2 - 2*x)*e^(3*x) + 2*(3*x^4 - 12*x^3 + 12*x^2 + 10)*e^(2*x) - 4*(x^6 - 6*x^5 + 12*x^4 - 8*x^3 + 1
0*x^2 - 20*x)*e^x + 2*(x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 26*x^4 - 40*x^3 + 40*x^2 - 4*(x^2 - 2*x)*e^(3*x) + 2*(3
*x^4 - 12*x^3 + 12*x^2 + 5)*e^(2*x) - 4*(x^6 - 6*x^5 + 12*x^4 - 8*x^3 + 5*x^2 - 10*x)*e^x + e^(4*x))*log(x - 4
) + 10*(x^4 - 4*x^3 + 4*x^2 - 2*(x^2 - 2*x)*e^x + (x^4 - 4*x^3 + 4*x^2 - 2*(x^2 - 2*x)*e^x + e^(2*x))*log(x -
4) + e^(2*x) + 10)*log(x) + 25*log(x)^2 + e^(4*x) + 100)/(log(x - 4)^2 + 2*log(x - 4) + 1)

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giac [B]  time = 0.58, size = 670, normalized size = 19.71 \begin {gather*} \frac {x^{8} \log \left (x - 4\right )^{2} + 2 \, x^{8} \log \left (x - 4\right ) - 8 \, x^{7} \log \left (x - 4\right )^{2} - 4 \, x^{6} e^{x} \log \left (x - 4\right )^{2} + x^{8} - 16 \, x^{7} \log \left (x - 4\right ) - 8 \, x^{6} e^{x} \log \left (x - 4\right ) + 24 \, x^{6} \log \left (x - 4\right )^{2} + 24 \, x^{5} e^{x} \log \left (x - 4\right )^{2} - 8 \, x^{7} - 4 \, x^{6} e^{x} + 48 \, x^{6} \log \left (x - 4\right ) + 48 \, x^{5} e^{x} \log \left (x - 4\right ) - 32 \, x^{5} \log \left (x - 4\right )^{2} + 6 \, x^{4} e^{\left (2 \, x\right )} \log \left (x - 4\right )^{2} - 48 \, x^{4} e^{x} \log \left (x - 4\right )^{2} + 24 \, x^{6} + 24 \, x^{5} e^{x} - 64 \, x^{5} \log \left (x - 4\right ) + 12 \, x^{4} e^{\left (2 \, x\right )} \log \left (x - 4\right ) - 96 \, x^{4} e^{x} \log \left (x - 4\right ) + 16 \, x^{4} \log \left (x - 4\right )^{2} - 24 \, x^{3} e^{\left (2 \, x\right )} \log \left (x - 4\right )^{2} + 32 \, x^{3} e^{x} \log \left (x - 4\right )^{2} + 10 \, x^{4} \log \left (x - 4\right ) \log \relax (x) - 32 \, x^{5} + 6 \, x^{4} e^{\left (2 \, x\right )} - 48 \, x^{4} e^{x} + 52 \, x^{4} \log \left (x - 4\right ) - 48 \, x^{3} e^{\left (2 \, x\right )} \log \left (x - 4\right ) + 64 \, x^{3} e^{x} \log \left (x - 4\right ) - 4 \, x^{2} e^{\left (3 \, x\right )} \log \left (x - 4\right )^{2} + 24 \, x^{2} e^{\left (2 \, x\right )} \log \left (x - 4\right )^{2} + 10 \, x^{4} \log \relax (x) - 40 \, x^{3} \log \left (x - 4\right ) \log \relax (x) - 20 \, x^{2} e^{x} \log \left (x - 4\right ) \log \relax (x) + 36 \, x^{4} - 24 \, x^{3} e^{\left (2 \, x\right )} + 32 \, x^{3} e^{x} - 80 \, x^{3} \log \left (x - 4\right ) - 8 \, x^{2} e^{\left (3 \, x\right )} \log \left (x - 4\right ) + 48 \, x^{2} e^{\left (2 \, x\right )} \log \left (x - 4\right ) - 40 \, x^{2} e^{x} \log \left (x - 4\right ) + 8 \, x e^{\left (3 \, x\right )} \log \left (x - 4\right )^{2} - 40 \, x^{3} \log \relax (x) - 20 \, x^{2} e^{x} \log \relax (x) + 40 \, x^{2} \log \left (x - 4\right ) \log \relax (x) + 40 \, x e^{x} \log \left (x - 4\right ) \log \relax (x) - 80 \, x^{3} - 4 \, x^{2} e^{\left (3 \, x\right )} + 24 \, x^{2} e^{\left (2 \, x\right )} - 40 \, x^{2} e^{x} + 80 \, x^{2} \log \left (x - 4\right ) + 16 \, x e^{\left (3 \, x\right )} \log \left (x - 4\right ) + 80 \, x e^{x} \log \left (x - 4\right ) + e^{\left (4 \, x\right )} \log \left (x - 4\right )^{2} + 40 \, x^{2} \log \relax (x) + 40 \, x e^{x} \log \relax (x) + 10 \, e^{\left (2 \, x\right )} \log \left (x - 4\right ) \log \relax (x) + 80 \, x^{2} + 8 \, x e^{\left (3 \, x\right )} + 80 \, x e^{x} + 2 \, e^{\left (4 \, x\right )} \log \left (x - 4\right ) + 20 \, e^{\left (2 \, x\right )} \log \left (x - 4\right ) + 10 \, e^{\left (2 \, x\right )} \log \relax (x) + 25 \, \log \relax (x)^{2} + e^{\left (4 \, x\right )} + 20 \, e^{\left (2 \, x\right )} + 100 \, \log \relax (x) + 100}{25 \, {\left (\log \left (x - 4\right )^{2} + 2 \, \log \left (x - 4\right ) + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-50*x*log(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2-160*x)*exp(x)+40*x^5-280*x^4+560*x^3
-320*x^2)*log(x-4)^2+((40*x^2-170*x)*exp(x)^2+(-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-64
0*x^2+50*x-200)*log(x-4)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*exp(x)+30*x^5-240*x^4+520*x^3-320*x^2-
150*x-200)*log(x)+((4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-1
92*x^2)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9-88*x^8+368*x^7-736*x^6+704*x^5-25
6*x^4)*log(x-4)^3+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*
x^3-536*x^2-150*x-40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012*x^3+200*x^2-480*x)*exp(x)+24*x^9
-264*x^8+1104*x^7-2208*x^6+2202*x^5-1408*x^4+1320*x^3-800*x^2)*log(x-4)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192
*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)*exp(x)^2+(-12*x^8+48*x^7+216*x^6
-1344*x^5+2128*x^4-832*x^3+320*x^2-960*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1
600*x^2+100*x-400)*log(x-4)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+
144*x^3-152*x^2-170*x-40)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-8
8*x^8+368*x^7-736*x^6+774*x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x)*log(x-4)^3+(75*x^2-300*x)*lo
g(x-4)^2+(75*x^2-300*x)*log(x-4)+25*x^2-100*x),x, algorithm="giac")

[Out]

1/25*(x^8*log(x - 4)^2 + 2*x^8*log(x - 4) - 8*x^7*log(x - 4)^2 - 4*x^6*e^x*log(x - 4)^2 + x^8 - 16*x^7*log(x -
4) - 8*x^6*e^x*log(x - 4) + 24*x^6*log(x - 4)^2 + 24*x^5*e^x*log(x - 4)^2 - 8*x^7 - 4*x^6*e^x + 48*x^6*log(x
- 4) + 48*x^5*e^x*log(x - 4) - 32*x^5*log(x - 4)^2 + 6*x^4*e^(2*x)*log(x - 4)^2 - 48*x^4*e^x*log(x - 4)^2 + 24
*x^6 + 24*x^5*e^x - 64*x^5*log(x - 4) + 12*x^4*e^(2*x)*log(x - 4) - 96*x^4*e^x*log(x - 4) + 16*x^4*log(x - 4)^
2 - 24*x^3*e^(2*x)*log(x - 4)^2 + 32*x^3*e^x*log(x - 4)^2 + 10*x^4*log(x - 4)*log(x) - 32*x^5 + 6*x^4*e^(2*x)
- 48*x^4*e^x + 52*x^4*log(x - 4) - 48*x^3*e^(2*x)*log(x - 4) + 64*x^3*e^x*log(x - 4) - 4*x^2*e^(3*x)*log(x - 4
)^2 + 24*x^2*e^(2*x)*log(x - 4)^2 + 10*x^4*log(x) - 40*x^3*log(x - 4)*log(x) - 20*x^2*e^x*log(x - 4)*log(x) +
36*x^4 - 24*x^3*e^(2*x) + 32*x^3*e^x - 80*x^3*log(x - 4) - 8*x^2*e^(3*x)*log(x - 4) + 48*x^2*e^(2*x)*log(x - 4
) - 40*x^2*e^x*log(x - 4) + 8*x*e^(3*x)*log(x - 4)^2 - 40*x^3*log(x) - 20*x^2*e^x*log(x) + 40*x^2*log(x - 4)*l
og(x) + 40*x*e^x*log(x - 4)*log(x) - 80*x^3 - 4*x^2*e^(3*x) + 24*x^2*e^(2*x) - 40*x^2*e^x + 80*x^2*log(x - 4)
+ 16*x*e^(3*x)*log(x - 4) + 80*x*e^x*log(x - 4) + e^(4*x)*log(x - 4)^2 + 40*x^2*log(x) + 40*x*e^x*log(x) + 10*
e^(2*x)*log(x - 4)*log(x) + 80*x^2 + 8*x*e^(3*x) + 80*x*e^x + 2*e^(4*x)*log(x - 4) + 20*e^(2*x)*log(x - 4) + 1
0*e^(2*x)*log(x) + 25*log(x)^2 + e^(4*x) + 20*e^(2*x) + 100*log(x) + 100)/(log(x - 4)^2 + 2*log(x - 4) + 1)

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maple [B]  time = 0.16, size = 330, normalized size = 9.71

method	result	size
risch	\(\frac {x^{8}}{25}-\frac {8 x^{7}}{25}+\frac {24 x^{6}}{25}-\frac {32 x^{5}}{25}+\frac {16 x^{4}}{25}+\frac {{\mathrm e}^{4 x}}{25}+\frac {8 x \,{\mathrm e}^{3 x}}{25}-\frac {4 x^{2} {\mathrm e}^{3 x}}{25}+\frac {24 \,{\mathrm e}^{2 x} x^{2}}{25}-\frac {24 \,{\mathrm e}^{2 x} x^{3}}{25}+\frac {6 \,{\mathrm e}^{2 x} x^{4}}{25}+\frac {32 \,{\mathrm e}^{x} x^{3}}{25}-\frac {48 \,{\mathrm e}^{x} x^{4}}{25}+\frac {24 x^{5} {\mathrm e}^{x}}{25}-\frac {4 x^{6} {\mathrm e}^{x}}{25}+\frac {20+8 x^{2} \ln \relax (x )-4 x^{2} {\mathrm e}^{x} \ln \relax (x )+8 x \,{\mathrm e}^{x} \ln \relax (x )+4 \,{\mathrm e}^{2 x}+20 \ln \relax (x )+5 \ln \relax (x )^{2}+4 x^{4}-16 x^{3}+16 x^{2}-8 x^{3} \ln \relax (x )+16 x^{2} \ln \left (x -4\right )-16 x^{3} \ln \left (x -4\right )+2 x^{4} \ln \relax (x )+16 \,{\mathrm e}^{x} x -8 \,{\mathrm e}^{x} x^{2}-4 \ln \relax (x ) {\mathrm e}^{x} \ln \left (x -4\right ) x^{2}+8 \ln \relax (x ) {\mathrm e}^{x} \ln \left (x -4\right ) x +4 \ln \left (x -4\right ) {\mathrm e}^{2 x}+2 \,{\mathrm e}^{2 x} \ln \relax (x )+4 \ln \left (x -4\right ) x^{4}+2 \ln \relax (x ) \ln \left (x -4\right ) x^{4}-8 \ln \relax (x ) \ln \left (x -4\right ) x^{3}+8 \ln \relax (x ) \ln \left (x -4\right ) x^{2}-8 \,{\mathrm e}^{x} \ln \left (x -4\right ) x^{2}+16 \,{\mathrm e}^{x} \ln \left (x -4\right ) x +2 \,{\mathrm e}^{2 x} \ln \relax (x ) \ln \left (x -4\right )}{5 \left (\ln \left (x -4\right )+1\right )^{2}}\)	\(330\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-50*x*ln(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2-160*x)*exp(x)+40*x^5-280*x^4+560*x^3-320*x^
2)*ln(x-4)^2+((40*x^2-170*x)*exp(x)^2+(-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-640*x^2+50
*x-200)*ln(x-4)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*exp(x)+30*x^5-240*x^4+520*x^3-320*x^2-150*x-200
)*ln(x)+((4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-192*x^2)*ex
p(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9-88*x^8+368*x^7-736*x^6+704*x^5-256*x^4)*ln(
x-4)^3+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-536*x^2
-150*x-40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012*x^3+200*x^2-480*x)*exp(x)+24*x^9-264*x^8+11
04*x^7-2208*x^6+2202*x^5-1408*x^4+1320*x^3-800*x^2)*ln(x-4)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3-168*x^2
-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+21
28*x^4-832*x^3+320*x^2-960*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1600*x^2+100*
x-400)*ln(x-4)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-152*x
^2-170*x-40)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-88*x^8+368*x^7
-736*x^6+774*x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x)*ln(x-4)^3+(75*x^2-300*x)*ln(x-4)^2+(75*x^
2-300*x)*ln(x-4)+25*x^2-100*x),x,method=_RETURNVERBOSE)

[Out]

1/25*x^8-8/25*x^7+24/25*x^6-32/25*x^5+16/25*x^4+1/25*exp(4*x)+8/25*x*exp(3*x)-4/25*x^2*exp(3*x)+24/25*exp(2*x)
*x^2-24/25*exp(2*x)*x^3+6/25*exp(2*x)*x^4+32/25*exp(x)*x^3-48/25*exp(x)*x^4+24/25*x^5*exp(x)-4/25*x^6*exp(x)+1
/5*(20+8*x^2*ln(x)-4*x^2*exp(x)*ln(x)+8*x*exp(x)*ln(x)+4*exp(2*x)+20*ln(x)+5*ln(x)^2+4*x^4-16*x^3+16*x^2-8*x^3
*ln(x)+16*x^2*ln(x-4)-16*x^3*ln(x-4)+2*x^4*ln(x)+16*exp(x)*x-8*exp(x)*x^2-4*ln(x)*exp(x)*ln(x-4)*x^2+8*ln(x)*e
xp(x)*ln(x-4)*x+4*ln(x-4)*exp(2*x)+2*exp(2*x)*ln(x)+4*ln(x-4)*x^4+2*ln(x)*ln(x-4)*x^4-8*ln(x)*ln(x-4)*x^3+8*ln
(x)*ln(x-4)*x^2-8*exp(x)*ln(x-4)*x^2+16*exp(x)*ln(x-4)*x+2*exp(2*x)*ln(x)*ln(x-4))/(ln(x-4)+1)^2

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maxima [B]  time = 0.57, size = 400, normalized size = 11.76 \begin {gather*} \frac {x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 36 \, x^{4} - 80 \, x^{3} + {\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 16 \, x^{4} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3}\right )} e^{x} + e^{\left (4 \, x\right )}\right )} \log \left (x - 4\right )^{2} + 80 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + 2 \, {\left (3 \, x^{4} - 12 \, x^{3} + 12 \, x^{2} + 5 \, \log \relax (x) + 10\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 6 \, x^{5} + 12 \, x^{4} - 8 \, x^{3} + 10 \, x^{2} + 5 \, {\left (x^{2} - 2 \, x\right )} \log \relax (x) - 20 \, x\right )} e^{x} + 2 \, {\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + 26 \, x^{4} - 40 \, x^{3} + 40 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} + {\left (6 \, x^{4} - 24 \, x^{3} + 24 \, x^{2} + 5 \, \log \relax (x) + 10\right )} e^{\left (2 \, x\right )} - 2 \, {\left (2 \, x^{6} - 12 \, x^{5} + 24 \, x^{4} - 16 \, x^{3} + 10 \, x^{2} + 5 \, {\left (x^{2} - 2 \, x\right )} \log \relax (x) - 20 \, x\right )} e^{x} + 5 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2}\right )} \log \relax (x) + e^{\left (4 \, x\right )}\right )} \log \left (x - 4\right ) + 10 \, {\left (x^{4} - 4 \, x^{3} + 4 \, x^{2} + 10\right )} \log \relax (x) + 25 \, \log \relax (x)^{2} + e^{\left (4 \, x\right )} + 100}{25 \, {\left (\log \left (x - 4\right )^{2} + 2 \, \log \left (x - 4\right ) + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-50*x*log(x)^2+(((20*x^2-80*x)*exp(x)^2+(-20*x^4+80*x^3+40*x^2-160*x)*exp(x)+40*x^5-280*x^4+560*x^3
-320*x^2)*log(x-4)^2+((40*x^2-170*x)*exp(x)^2+(-40*x^4+180*x^3+40*x^2-320*x)*exp(x)+70*x^5-520*x^4+1080*x^3-64
0*x^2+50*x-200)*log(x-4)+(20*x^2-90*x)*exp(x)^2+(-20*x^4+100*x^3-160*x)*exp(x)+30*x^5-240*x^4+520*x^3-320*x^2-
150*x-200)*log(x)+((4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+144*x^3-1
92*x^2)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+736*x^4-384*x^3)*exp(x)+8*x^9-88*x^8+368*x^7-736*x^6+704*x^5-25
6*x^4)*log(x-4)^3+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*
x^3-536*x^2-150*x-40)*exp(x)^2+(-12*x^8+48*x^7+216*x^6-1344*x^5+2168*x^4-1012*x^3+200*x^2-480*x)*exp(x)+24*x^9
-264*x^8+1104*x^7-2208*x^6+2202*x^5-1408*x^4+1320*x^3-800*x^2)*log(x-4)^2+((12*x^2-48*x)*exp(x)^4+(-36*x^4+192
*x^3-168*x^2-96*x)*exp(x)^3+(36*x^6-216*x^5+216*x^4+432*x^3-496*x^2-320*x-80)*exp(x)^2+(-12*x^8+48*x^7+216*x^6
-1344*x^5+2128*x^4-832*x^3+320*x^2-960*x)*exp(x)+24*x^9-264*x^8+1104*x^7-2208*x^6+2272*x^5-1968*x^4+2560*x^3-1
600*x^2+100*x-400)*log(x-4)+(4*x^2-16*x)*exp(x)^4+(-12*x^4+64*x^3-56*x^2-32*x)*exp(x)^3+(12*x^6-72*x^5+72*x^4+
144*x^3-152*x^2-170*x-40)*exp(x)^2+(-4*x^8+16*x^7+72*x^6-448*x^5+696*x^4-204*x^3+120*x^2-480*x)*exp(x)+8*x^9-8
8*x^8+368*x^7-736*x^6+774*x^5-816*x^4+1240*x^3-800*x^2-100*x-400)/((25*x^2-100*x)*log(x-4)^3+(75*x^2-300*x)*lo
g(x-4)^2+(75*x^2-300*x)*log(x-4)+25*x^2-100*x),x, algorithm="maxima")

[Out]

1/25*(x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 36*x^4 - 80*x^3 + (x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 16*x^4 - 4*(x^2 - 2*x
)*e^(3*x) + 6*(x^4 - 4*x^3 + 4*x^2)*e^(2*x) - 4*(x^6 - 6*x^5 + 12*x^4 - 8*x^3)*e^x + e^(4*x))*log(x - 4)^2 + 8
0*x^2 - 4*(x^2 - 2*x)*e^(3*x) + 2*(3*x^4 - 12*x^3 + 12*x^2 + 5*log(x) + 10)*e^(2*x) - 4*(x^6 - 6*x^5 + 12*x^4
- 8*x^3 + 10*x^2 + 5*(x^2 - 2*x)*log(x) - 20*x)*e^x + 2*(x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 26*x^4 - 40*x^3 + 40*
x^2 - 4*(x^2 - 2*x)*e^(3*x) + (6*x^4 - 24*x^3 + 24*x^2 + 5*log(x) + 10)*e^(2*x) - 2*(2*x^6 - 12*x^5 + 24*x^4 -
16*x^3 + 10*x^2 + 5*(x^2 - 2*x)*log(x) - 20*x)*e^x + 5*(x^4 - 4*x^3 + 4*x^2)*log(x) + e^(4*x))*log(x - 4) + 1
0*(x^4 - 4*x^3 + 4*x^2 + 10)*log(x) + 25*log(x)^2 + e^(4*x) + 100)/(log(x - 4)^2 + 2*log(x - 4) + 1)

________________________________________________________________________________________

mupad [B]  time = 5.90, size = 1647, normalized size = 48.44 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((100*x + exp(4*x)*(16*x - 4*x^2) + 50*x*log(x)^2 + log(x - 4)^3*(exp(4*x)*(16*x - 4*x^2) - exp(2*x)*(144*x
^3 - 192*x^2 + 72*x^4 - 72*x^5 + 12*x^6) + exp(3*x)*(32*x + 56*x^2 - 64*x^3 + 12*x^4) + 256*x^4 - 704*x^5 + 73
6*x^6 - 368*x^7 + 88*x^8 - 8*x^9 + exp(x)*(384*x^3 - 736*x^4 + 448*x^5 - 72*x^6 - 16*x^7 + 4*x^8)) + log(x - 4
)^2*(exp(4*x)*(48*x - 12*x^2) + exp(3*x)*(96*x + 168*x^2 - 192*x^3 + 36*x^4) + 800*x^2 - 1320*x^3 + 1408*x^4 -
2202*x^5 + 2208*x^6 - 1104*x^7 + 264*x^8 - 24*x^9 + exp(2*x)*(150*x + 536*x^2 - 432*x^3 - 216*x^4 + 216*x^5 -
36*x^6 + 40) + exp(x)*(480*x - 200*x^2 + 1012*x^3 - 2168*x^4 + 1344*x^5 - 216*x^6 - 48*x^7 + 12*x^8)) + exp(3
*x)*(32*x + 56*x^2 - 64*x^3 + 12*x^4) + log(x)*(150*x + exp(2*x)*(90*x - 20*x^2) + log(x - 4)^2*(exp(2*x)*(80*
x - 20*x^2) + exp(x)*(160*x - 40*x^2 - 80*x^3 + 20*x^4) + 320*x^2 - 560*x^3 + 280*x^4 - 40*x^5) + 320*x^2 - 52
0*x^3 + 240*x^4 - 30*x^5 + log(x - 4)*(exp(2*x)*(170*x - 40*x^2) - 50*x + exp(x)*(320*x - 40*x^2 - 180*x^3 + 4
0*x^4) + 640*x^2 - 1080*x^3 + 520*x^4 - 70*x^5 + 200) + exp(x)*(160*x - 100*x^3 + 20*x^4) + 200) + 800*x^2 - 1
240*x^3 + 816*x^4 - 774*x^5 + 736*x^6 - 368*x^7 + 88*x^8 - 8*x^9 + exp(2*x)*(170*x + 152*x^2 - 144*x^3 - 72*x^
4 + 72*x^5 - 12*x^6 + 40) + log(x - 4)*(exp(4*x)*(48*x - 12*x^2) - 100*x + exp(3*x)*(96*x + 168*x^2 - 192*x^3
+ 36*x^4) + 1600*x^2 - 2560*x^3 + 1968*x^4 - 2272*x^5 + 2208*x^6 - 1104*x^7 + 264*x^8 - 24*x^9 + exp(2*x)*(320
*x + 496*x^2 - 432*x^3 - 216*x^4 + 216*x^5 - 36*x^6 + 80) + exp(x)*(960*x - 320*x^2 + 832*x^3 - 2128*x^4 + 134
4*x^5 - 216*x^6 - 48*x^7 + 12*x^8) + 400) + exp(x)*(480*x - 120*x^2 + 204*x^3 - 696*x^4 + 448*x^5 - 72*x^6 - 1
6*x^7 + 4*x^8) + 400)/(100*x + log(x - 4)*(300*x - 75*x^2) + log(x - 4)^3*(100*x - 25*x^2) + log(x - 4)^2*(300
*x - 75*x^2) - 25*x^2),x)

[Out]

exp(4*x)/25 - (1552*x)/5 + (448*log(x - 4))/5 + (128*log(x))/5 + exp(3*x)*((8*x)/25 - (4*x^2)/25) + log(x)*(ex
p(2*x)*((4*x^2)/5 - (26*x)/5 + 8) + exp(x)*((28*x^2)/5 - (84*x)/5 + (6*x^3)/5 - (2*x^4)/5 + 16/5) + (4*x + (10
88*x^3)/5 - 560*x^4 + (1836*x^5)/5 - (336*x^6)/5 - 16)/x^2 - ((1632*x^3)/5 - 672*x^4 + 408*x^5 - 72*x^6)/x^2)
- ((40*x - 16*exp(2*x) - 80*log(x) + 64*x*exp(2*x) + 32*x^2*exp(x) - 236*x^3*exp(x) + 74*x^4*exp(x) + 12*x^5*e
xp(x) - 4*x^6*exp(x) + 123*x^2*log(x) - 512*x^3*log(x) + 500*x^4*log(x) - 172*x^5*log(x) + 19*x^6*log(x) + 63*
x^2*exp(2*x) - 52*x^3*exp(2*x) + 8*x^4*exp(2*x) + 64*x*exp(x) + 40*x*log(x) + 443*x^2 - 1472*x^3 + 1324*x^4 -
436*x^5 + 47*x^6 + 47*x^2*exp(2*x)*log(x) - 28*x^3*exp(2*x)*log(x) + 4*x^4*exp(2*x)*log(x) + 32*x^2*exp(x)*log
(x) - 92*x^3*exp(x)*log(x) + 22*x^4*exp(x)*log(x) + 8*x^5*exp(x)*log(x) - 2*x^6*exp(x)*log(x) - 80)/(5*x^2) +
(log(x - 4)*(x - 4)*(5*x + 8*exp(2*x) + 20*log(x) - 31*x*exp(2*x) - 36*x^2*exp(x) + 110*x^3*exp(x) - 4*x^4*exp
(x) - 8*x^5*exp(x) - 64*x^2*log(x) + 232*x^3*log(x) - 180*x^4*log(x) + 36*x^5*log(x) - 44*x^2*exp(2*x) + 16*x^
3*exp(2*x) - 32*x*exp(x) - 224*x^2 + 660*x^3 - 468*x^4 + 89*x^5 - 26*x^2*exp(2*x)*log(x) + 8*x^3*exp(2*x)*log(
x) - 20*x^2*exp(x)*log(x) + 40*x^3*exp(x)*log(x) + 2*x^4*exp(x)*log(x) - 4*x^5*exp(x)*log(x) + 20))/(5*x^2) -
(2*log(x - 4)^2*(x - 4)*(8*x*exp(2*x) - 2*exp(2*x) + 12*x^2*exp(x) - 28*x^3*exp(x) + 2*x^5*exp(x) + 16*x^2*log
(x) - 56*x^3*log(x) + 42*x^4*log(x) - 8*x^5*log(x) + 12*x^2*exp(2*x) - 4*x^3*exp(2*x) + 8*x*exp(x) + 56*x^2 -
160*x^3 + 110*x^4 - 20*x^5 + 7*x^2*exp(2*x)*log(x) - 2*x^3*exp(2*x)*log(x) + 6*x^2*exp(x)*log(x) - 10*x^3*exp(
x)*log(x) - x^4*exp(x)*log(x) + x^5*exp(x)*log(x)))/(5*x^2))/(log(x - 4) + 1) - log(x - 4)*((1920*x^4 - 1376*x
^5 + (1264*x^6)/3 - (196*x^7)/3 + 4*x^8)/(5*x^3*(x - 4)) - log(x)*((exp(2*x)*(56*x - 30*x^2 + 4*x^3))/(5*x) -
(480*x^2 - 448*x^3 + 148*x^4 - 16*x^5)/(5*x) + (exp(x)*(48*x - 92*x^2 + 12*x^3 + 10*x^4 - 2*x^5))/(5*x) + 128/
5) - (7488*x^4 - 7568*x^5 + (9424*x^6)/3 - (1816*x^7)/3 + 44*x^8)/(5*x^3*(x - 4)) + (exp(x)*(256*x^2 - 64*x^3)
)/(5*x^3*(x - 4)) - (exp(2*x)*(64*x - 288*x^2 + 68*x^3))/(5*x^3*(x - 4)) + (exp(2*x)*(64*x^3 - 24*x^4 + 2*x^5)
)/(5*x^3*(x - 4)) + (exp(x)*(288*x^3 + 8*x^4 - 84*x^5 + 24*x^6 - 2*x^7))/(5*x^3*(x - 4)) + (exp(2*x)*(256*x^3
- 280*x^4 + 86*x^5 - 8*x^6))/(5*x^3*(x - 4)) + (exp(x)*(32*x^3 - 1080*x^4 + 556*x^5 - 16*x^6 - 30*x^7 + 4*x^8)
)/(5*x^3*(x - 4))) - 16/x^2 + (1464*x^2)/5 - (508*x^3)/5 + (306*x^4)/25 - (32*x^5)/25 + (24*x^6)/25 - (8*x^7)/
25 + x^8/25 + ((10*x + 4*exp(2*x) + 20*log(x) + 17*x*exp(2*x) - 12*x^2*exp(x) - 18*x^3*exp(x) + 4*x^4*exp(x) +
5*x*log(x)^2 + 32*x^2*log(x) - 52*x^3*log(x) + 24*x^4*log(x) - 3*x^5*log(x) - 4*x^2*exp(2*x) + 48*x*exp(x) +
15*x*log(x) + 80*x^2 - 124*x^3 + 56*x^4 - 7*x^5 - 2*x^2*exp(2*x)*log(x) + 16*x*exp(x)*log(x) + 9*x*exp(2*x)*lo
g(x) - 10*x^3*exp(x)*log(x) + 2*x^4*exp(x)*log(x) + 40)/(5*x) + (log(x - 4)*(8*exp(2*x) - 10*x + 20*log(x) + 3
2*x*exp(2*x) - 32*x^2*exp(x) - 32*x^3*exp(x) + 8*x^4*exp(x) + 64*x^2*log(x) - 108*x^3*log(x) + 52*x^4*log(x) -
7*x^5*log(x) - 8*x^2*exp(2*x) + 96*x*exp(x) - 5*x*log(x) + 160*x^2 - 256*x^3 + 120*x^4 - 16*x^5 - 4*x^2*exp(2
*x)*log(x) + 32*x*exp(x)*log(x) + 17*x*exp(2*x)*log(x) - 4*x^2*exp(x)*log(x) - 18*x^3*exp(x)*log(x) + 4*x^4*ex
p(x)*log(x) + 40))/(5*x) - (log(x - 4)^2*(x - 4)*(2*x + exp(x) - x^2)*(10*x + exp(x) - 4*x^2*log(x) + 4*x*exp(
x) + 4*x*log(x) - 9*x^2 + 2*x*exp(x)*log(x)))/(5*x))/(2*log(x - 4) + log(x - 4)^2 + 1) - (exp(x)*((16*x)/5 + (
208*x^2)/5 - (84*x^3)/5 - (72*x^4)/25 + (68*x^5)/25 - (24*x^6)/25 + (4*x^7)/25 - 64/5))/x + (exp(2*x)*(12*x +
10*x^2 - (48*x^3)/5 + (64*x^4)/25 - (24*x^5)/25 + (6*x^6)/25 - 16/5))/x^2

________________________________________________________________________________________

sympy [B]  time = 1.62, size = 532, normalized size = 15.65 \begin {gather*} \frac {x^{8}}{25} - \frac {8 x^{7}}{25} + \frac {24 x^{6}}{25} - \frac {32 x^{5}}{25} + \frac {16 x^{4}}{25} + \frac {\left (15625 \log {\left (x - 4 \right )}^{2} + 31250 \log {\left (x - 4 \right )} + 15625\right ) e^{4 x} + \left (- 62500 x^{2} \log {\left (x - 4 \right )}^{2} - 125000 x^{2} \log {\left (x - 4 \right )} - 62500 x^{2} + 125000 x \log {\left (x - 4 \right )}^{2} + 250000 x \log {\left (x - 4 \right )} + 125000 x\right ) e^{3 x} + \left (93750 x^{4} \log {\left (x - 4 \right )}^{2} + 187500 x^{4} \log {\left (x - 4 \right )} + 93750 x^{4} - 375000 x^{3} \log {\left (x - 4 \right )}^{2} - 750000 x^{3} \log {\left (x - 4 \right )} - 375000 x^{3} + 375000 x^{2} \log {\left (x - 4 \right )}^{2} + 750000 x^{2} \log {\left (x - 4 \right )} + 375000 x^{2} + 156250 \log {\relax (x )} \log {\left (x - 4 \right )} + 156250 \log {\relax (x )} + 312500 \log {\left (x - 4 \right )} + 312500\right ) e^{2 x} + \left (- 62500 x^{6} \log {\left (x - 4 \right )}^{2} - 125000 x^{6} \log {\left (x - 4 \right )} - 62500 x^{6} + 375000 x^{5} \log {\left (x - 4 \right )}^{2} + 750000 x^{5} \log {\left (x - 4 \right )} + 375000 x^{5} - 750000 x^{4} \log {\left (x - 4 \right )}^{2} - 1500000 x^{4} \log {\left (x - 4 \right )} - 750000 x^{4} + 500000 x^{3} \log {\left (x - 4 \right )}^{2} + 1000000 x^{3} \log {\left (x - 4 \right )} + 500000 x^{3} - 312500 x^{2} \log {\relax (x )} \log {\left (x - 4 \right )} - 312500 x^{2} \log {\relax (x )} - 625000 x^{2} \log {\left (x - 4 \right )} - 625000 x^{2} + 625000 x \log {\relax (x )} \log {\left (x - 4 \right )} + 625000 x \log {\relax (x )} + 1250000 x \log {\left (x - 4 \right )} + 1250000 x\right ) e^{x}}{390625 \log {\left (x - 4 \right )}^{2} + 781250 \log {\left (x - 4 \right )} + 390625} + \frac {2 x^{4} \log {\relax (x )} + 4 x^{4} - 8 x^{3} \log {\relax (x )} - 16 x^{3} + 8 x^{2} \log {\relax (x )} + 16 x^{2} + \left (2 x^{4} \log {\relax (x )} + 4 x^{4} - 8 x^{3} \log {\relax (x )} - 16 x^{3} + 8 x^{2} \log {\relax (x )} + 16 x^{2}\right ) \log {\left (x - 4 \right )} + 5 \log {\relax (x )}^{2} + 20 \log {\relax (x )} + 20}{5 \log {\left (x - 4 \right )}^{2} + 10 \log {\left (x - 4 \right )} + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-50*x*ln(x)**2+(((20*x**2-80*x)*exp(x)**2+(-20*x**4+80*x**3+40*x**2-160*x)*exp(x)+40*x**5-280*x**4+
560*x**3-320*x**2)*ln(x-4)**2+((40*x**2-170*x)*exp(x)**2+(-40*x**4+180*x**3+40*x**2-320*x)*exp(x)+70*x**5-520*
x**4+1080*x**3-640*x**2+50*x-200)*ln(x-4)+(20*x**2-90*x)*exp(x)**2+(-20*x**4+100*x**3-160*x)*exp(x)+30*x**5-24
0*x**4+520*x**3-320*x**2-150*x-200)*ln(x)+((4*x**2-16*x)*exp(x)**4+(-12*x**4+64*x**3-56*x**2-32*x)*exp(x)**3+(
12*x**6-72*x**5+72*x**4+144*x**3-192*x**2)*exp(x)**2+(-4*x**8+16*x**7+72*x**6-448*x**5+736*x**4-384*x**3)*exp(
x)+8*x**9-88*x**8+368*x**7-736*x**6+704*x**5-256*x**4)*ln(x-4)**3+((12*x**2-48*x)*exp(x)**4+(-36*x**4+192*x**3
-168*x**2-96*x)*exp(x)**3+(36*x**6-216*x**5+216*x**4+432*x**3-536*x**2-150*x-40)*exp(x)**2+(-12*x**8+48*x**7+2
16*x**6-1344*x**5+2168*x**4-1012*x**3+200*x**2-480*x)*exp(x)+24*x**9-264*x**8+1104*x**7-2208*x**6+2202*x**5-14
08*x**4+1320*x**3-800*x**2)*ln(x-4)**2+((12*x**2-48*x)*exp(x)**4+(-36*x**4+192*x**3-168*x**2-96*x)*exp(x)**3+(
36*x**6-216*x**5+216*x**4+432*x**3-496*x**2-320*x-80)*exp(x)**2+(-12*x**8+48*x**7+216*x**6-1344*x**5+2128*x**4
-832*x**3+320*x**2-960*x)*exp(x)+24*x**9-264*x**8+1104*x**7-2208*x**6+2272*x**5-1968*x**4+2560*x**3-1600*x**2+
100*x-400)*ln(x-4)+(4*x**2-16*x)*exp(x)**4+(-12*x**4+64*x**3-56*x**2-32*x)*exp(x)**3+(12*x**6-72*x**5+72*x**4+
144*x**3-152*x**2-170*x-40)*exp(x)**2+(-4*x**8+16*x**7+72*x**6-448*x**5+696*x**4-204*x**3+120*x**2-480*x)*exp(
x)+8*x**9-88*x**8+368*x**7-736*x**6+774*x**5-816*x**4+1240*x**3-800*x**2-100*x-400)/((25*x**2-100*x)*ln(x-4)**
3+(75*x**2-300*x)*ln(x-4)**2+(75*x**2-300*x)*ln(x-4)+25*x**2-100*x),x)

[Out]

x**8/25 - 8*x**7/25 + 24*x**6/25 - 32*x**5/25 + 16*x**4/25 + ((15625*log(x - 4)**2 + 31250*log(x - 4) + 15625)
*exp(4*x) + (-62500*x**2*log(x - 4)**2 - 125000*x**2*log(x - 4) - 62500*x**2 + 125000*x*log(x - 4)**2 + 250000
*x*log(x - 4) + 125000*x)*exp(3*x) + (93750*x**4*log(x - 4)**2 + 187500*x**4*log(x - 4) + 93750*x**4 - 375000*
x**3*log(x - 4)**2 - 750000*x**3*log(x - 4) - 375000*x**3 + 375000*x**2*log(x - 4)**2 + 750000*x**2*log(x - 4)
+ 375000*x**2 + 156250*log(x)*log(x - 4) + 156250*log(x) + 312500*log(x - 4) + 312500)*exp(2*x) + (-62500*x**
6*log(x - 4)**2 - 125000*x**6*log(x - 4) - 62500*x**6 + 375000*x**5*log(x - 4)**2 + 750000*x**5*log(x - 4) + 3
75000*x**5 - 750000*x**4*log(x - 4)**2 - 1500000*x**4*log(x - 4) - 750000*x**4 + 500000*x**3*log(x - 4)**2 + 1
000000*x**3*log(x - 4) + 500000*x**3 - 312500*x**2*log(x)*log(x - 4) - 312500*x**2*log(x) - 625000*x**2*log(x
- 4) - 625000*x**2 + 625000*x*log(x)*log(x - 4) + 625000*x*log(x) + 1250000*x*log(x - 4) + 1250000*x)*exp(x))/
(390625*log(x - 4)**2 + 781250*log(x - 4) + 390625) + (2*x**4*log(x) + 4*x**4 - 8*x**3*log(x) - 16*x**3 + 8*x*
*2*log(x) + 16*x**2 + (2*x**4*log(x) + 4*x**4 - 8*x**3*log(x) - 16*x**3 + 8*x**2*log(x) + 16*x**2)*log(x - 4)
+ 5*log(x)**2 + 20*log(x) + 20)/(5*log(x - 4)**2 + 10*log(x - 4) + 5)

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