3.89.22 \(\int \frac {(20 x-996 x^2+11900 x^3+12380 x^4+4992 x^5+1000 x^6+100 x^7+4 x^8+e^{x^2} (-40+1992 x-23800 x^2-24760 x^3-9984 x^4-2000 x^5-200 x^6-8 x^7)) \log (2 x^2)+(-5 x-5 x^2+3225 x^3+3165 x^4+1254 x^5+250 x^6+25 x^7+x^8+e^{x^2} (508 x-12380 x^2-13516 x^3+6896 x^4+11380 x^5+4892 x^6+996 x^7+100 x^8+4 x^9)) \log ^2(2 x^2)}{3125 x^3+3125 x^4+1250 x^5+250 x^6+25 x^7+x^8+e^{2 x^2} (12500 x+12500 x^2+5000 x^3+1000 x^4+100 x^5+4 x^6)+e^{x^2} (-12500 x^2-12500 x^3-5000 x^4-1000 x^5-100 x^6-4 x^7)} \, dx\)

Optimal. Leaf size=31 \[ \frac {\left (-x+\frac {1}{(5+x)^2}\right )^2 \log ^2\left (2 x^2\right )}{-2 e^{x^2}+x} \]

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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[((20*x - 996*x^2 + 11900*x^3 + 12380*x^4 + 4992*x^5 + 1000*x^6 + 100*x^7 + 4*x^8 + E^x^2*(-40 + 1992*x - 2
3800*x^2 - 24760*x^3 - 9984*x^4 - 2000*x^5 - 200*x^6 - 8*x^7))*Log[2*x^2] + (-5*x - 5*x^2 + 3225*x^3 + 3165*x^
4 + 1254*x^5 + 250*x^6 + 25*x^7 + x^8 + E^x^2*(508*x - 12380*x^2 - 13516*x^3 + 6896*x^4 + 11380*x^5 + 4892*x^6
+ 996*x^7 + 100*x^8 + 4*x^9))*Log[2*x^2]^2)/(3125*x^3 + 3125*x^4 + 1250*x^5 + 250*x^6 + 25*x^7 + x^8 + E^(2*x
^2)*(12500*x + 12500*x^2 + 5000*x^3 + 1000*x^4 + 100*x^5 + 4*x^6) + E^x^2*(-12500*x^2 - 12500*x^3 - 5000*x^4 -
1000*x^5 - 100*x^6 - 4*x^7)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.16, size = 43, normalized size = 1.39 \begin {gather*} -\frac {\left (-1+25 x+10 x^2+x^3\right )^2 \log ^2\left (2 x^2\right )}{\left (2 e^{x^2}-x\right ) (5+x)^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((20*x - 996*x^2 + 11900*x^3 + 12380*x^4 + 4992*x^5 + 1000*x^6 + 100*x^7 + 4*x^8 + E^x^2*(-40 + 1992
*x - 23800*x^2 - 24760*x^3 - 9984*x^4 - 2000*x^5 - 200*x^6 - 8*x^7))*Log[2*x^2] + (-5*x - 5*x^2 + 3225*x^3 + 3
165*x^4 + 1254*x^5 + 250*x^6 + 25*x^7 + x^8 + E^x^2*(508*x - 12380*x^2 - 13516*x^3 + 6896*x^4 + 11380*x^5 + 48
92*x^6 + 996*x^7 + 100*x^8 + 4*x^9))*Log[2*x^2]^2)/(3125*x^3 + 3125*x^4 + 1250*x^5 + 250*x^6 + 25*x^7 + x^8 +
E^(2*x^2)*(12500*x + 12500*x^2 + 5000*x^3 + 1000*x^4 + 100*x^5 + 4*x^6) + E^x^2*(-12500*x^2 - 12500*x^3 - 5000
*x^4 - 1000*x^5 - 100*x^6 - 4*x^7)),x]

[Out]

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

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fricas [B]  time = 0.60, size = 85, normalized size = 2.74 \begin {gather*} \frac {{\left (x^{6} + 20 \, x^{5} + 150 \, x^{4} + 498 \, x^{3} + 605 \, x^{2} - 50 \, x + 1\right )} \log \left (2 \, x^{2}\right )^{2}}{x^{5} + 20 \, x^{4} + 150 \, x^{3} + 500 \, x^{2} - 2 \, {\left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + 625\right )} e^{\left (x^{2}\right )} + 625 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^9+100*x^8+996*x^7+4892*x^6+11380*x^5+6896*x^4-13516*x^3-12380*x^2+508*x)*exp(x^2)+x^8+25*x^7+
250*x^6+1254*x^5+3165*x^4+3225*x^3-5*x^2-5*x)*log(2*x^2)^2+((-8*x^7-200*x^6-2000*x^5-9984*x^4-24760*x^3-23800*
x^2+1992*x-40)*exp(x^2)+4*x^8+100*x^7+1000*x^6+4992*x^5+12380*x^4+11900*x^3-996*x^2+20*x)*log(2*x^2))/((4*x^6+
100*x^5+1000*x^4+5000*x^3+12500*x^2+12500*x)*exp(x^2)^2+(-4*x^7-100*x^6-1000*x^5-5000*x^4-12500*x^3-12500*x^2)
*exp(x^2)+x^8+25*x^7+250*x^6+1250*x^5+3125*x^4+3125*x^3),x, algorithm="fricas")

[Out]

(x^6 + 20*x^5 + 150*x^4 + 498*x^3 + 605*x^2 - 50*x + 1)*log(2*x^2)^2/(x^5 + 20*x^4 + 150*x^3 + 500*x^2 - 2*(x^
4 + 20*x^3 + 150*x^2 + 500*x + 625)*e^(x^2) + 625*x)

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giac [B]  time = 0.58, size = 149, normalized size = 4.81 \begin {gather*} \frac {x^{6} \log \left (2 \, x^{2}\right )^{2} + 20 \, x^{5} \log \left (2 \, x^{2}\right )^{2} + 150 \, x^{4} \log \left (2 \, x^{2}\right )^{2} + 498 \, x^{3} \log \left (2 \, x^{2}\right )^{2} + 605 \, x^{2} \log \left (2 \, x^{2}\right )^{2} - 50 \, x \log \left (2 \, x^{2}\right )^{2} + \log \left (2 \, x^{2}\right )^{2}}{x^{5} - 2 \, x^{4} e^{\left (x^{2}\right )} + 20 \, x^{4} - 40 \, x^{3} e^{\left (x^{2}\right )} + 150 \, x^{3} - 300 \, x^{2} e^{\left (x^{2}\right )} + 500 \, x^{2} - 1000 \, x e^{\left (x^{2}\right )} + 625 \, x - 1250 \, e^{\left (x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^9+100*x^8+996*x^7+4892*x^6+11380*x^5+6896*x^4-13516*x^3-12380*x^2+508*x)*exp(x^2)+x^8+25*x^7+
250*x^6+1254*x^5+3165*x^4+3225*x^3-5*x^2-5*x)*log(2*x^2)^2+((-8*x^7-200*x^6-2000*x^5-9984*x^4-24760*x^3-23800*
x^2+1992*x-40)*exp(x^2)+4*x^8+100*x^7+1000*x^6+4992*x^5+12380*x^4+11900*x^3-996*x^2+20*x)*log(2*x^2))/((4*x^6+
100*x^5+1000*x^4+5000*x^3+12500*x^2+12500*x)*exp(x^2)^2+(-4*x^7-100*x^6-1000*x^5-5000*x^4-12500*x^3-12500*x^2)
*exp(x^2)+x^8+25*x^7+250*x^6+1250*x^5+3125*x^4+3125*x^3),x, algorithm="giac")

[Out]

(x^6*log(2*x^2)^2 + 20*x^5*log(2*x^2)^2 + 150*x^4*log(2*x^2)^2 + 498*x^3*log(2*x^2)^2 + 605*x^2*log(2*x^2)^2 -
50*x*log(2*x^2)^2 + log(2*x^2)^2)/(x^5 - 2*x^4*e^(x^2) + 20*x^4 - 40*x^3*e^(x^2) + 150*x^3 - 300*x^2*e^(x^2)
+ 500*x^2 - 1000*x*e^(x^2) + 625*x - 1250*e^(x^2))

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maple [C]  time = 1.01, size = 1812, normalized size = 58.45

method	result	size
risch	\(\frac {4 \left (x^{6}+20 x^{5}+150 x^{4}+498 x^{3}+605 x^{2}-50 x +1\right ) \ln \relax (x )^{2}}{\left (x^{4}+20 x^{3}+150 x^{2}+500 x +625\right ) \left (x -2 \,{\mathrm e}^{x^{2}}\right )}+\frac {2 \left (2 \ln \relax (2)+300 x^{4} \ln \relax (2)+40 x^{5} \ln \relax (2)+2 x^{6} \ln \relax (2)-100 x \ln \relax (2)+1210 x^{2} \ln \relax (2)+996 x^{3} \ln \relax (2)-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-i \pi \,x^{6} \mathrm {csgn}\left (i x^{2}\right )^{3}-20 i \pi \,x^{5} \mathrm {csgn}\left (i x^{2}\right )^{3}-150 i \pi \,x^{4} \mathrm {csgn}\left (i x^{2}\right )^{3}-498 i \pi \,x^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+50 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}-605 i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}-20 i \pi \,x^{5} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+40 i \pi \,x^{5} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-150 i \pi \,x^{4} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+300 i \pi \,x^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-498 i \pi \,x^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+996 i \pi \,x^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \,x^{6} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,x^{6} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+50 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-100 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-605 i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+1210 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}\right ) \ln \relax (x )}{\left (5+x \right ) \left (x^{3}+15 x^{2}+75 x +125\right ) \left (x -2 \,{\mathrm e}^{x^{2}}\right )}+\frac {4 x^{6} \ln \relax (2)^{2}+4 \ln \relax (2)^{2}+80 x^{5} \ln \relax (2)^{2}+600 x^{4} \ln \relax (2)^{2}+1992 x^{3} \ln \relax (2)^{2}-200 x \ln \relax (2)^{2}+2420 x^{2} \ln \relax (2)^{2}-605 \pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+2420 \pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-3630 \pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+2420 \pi ^{2} x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-605 \pi ^{2} x^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4}+50 x \,\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}-498 \pi ^{2} x^{3} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+1992 \pi ^{2} x^{3} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-\pi ^{2} x^{6} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+4 \pi ^{2} x^{6} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-6 \pi ^{2} x^{6} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+4 \pi ^{2} x^{6} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-4 i \ln \relax (2) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-20 \pi ^{2} x^{5} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+80 \pi ^{2} x^{5} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-120 \pi ^{2} x^{5} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+80 \pi ^{2} x^{5} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-150 \pi ^{2} x^{4} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+600 \pi ^{2} x^{4} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-1992 i \pi \ln \relax (2) x^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-2420 i \pi \ln \relax (2) x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}+200 i \pi \ln \relax (2) x \mathrm {csgn}\left (i x^{2}\right )^{3}-4 i \pi \ln \relax (2) x^{6} \mathrm {csgn}\left (i x^{2}\right )^{3}-80 i \pi \ln \relax (2) x^{5} \mathrm {csgn}\left (i x^{2}\right )^{3}-600 i \pi \ln \relax (2) x^{4} \mathrm {csgn}\left (i x^{2}\right )^{3}-4 i \ln \relax (2) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+8 i \ln \relax (2) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\pi ^{2} x^{6} \mathrm {csgn}\left (i x^{2}\right )^{6}-20 \pi ^{2} x^{5} \mathrm {csgn}\left (i x^{2}\right )^{6}-150 \pi ^{2} x^{4} \mathrm {csgn}\left (i x^{2}\right )^{6}+4 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right )-6 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}-498 \pi ^{2} x^{3} \mathrm {csgn}\left (i x^{2}\right )^{6}+50 x \,\pi ^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}-200 x \,\pi ^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}+300 x \,\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}-200 x \,\pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}+4 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3}+1992 \pi ^{2} x^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-2988 \pi ^{2} x^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}-900 \pi ^{2} x^{4} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+600 \pi ^{2} x^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}+200 i \pi \ln \relax (2) x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-400 i \pi \ln \relax (2) x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-80 i \pi \ln \relax (2) x^{5} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+160 i \pi \ln \relax (2) x^{5} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-600 i \pi \ln \relax (2) x^{4} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+1200 i \pi \ln \relax (2) x^{4} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-1992 i \pi \ln \relax (2) x^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+3984 i \pi \ln \relax (2) x^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-2420 i \pi \ln \relax (2) x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+4840 i \pi \ln \relax (2) x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-4 i \pi \ln \relax (2) x^{6} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+8 i \pi \ln \relax (2) x^{6} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}}{4 \left (x^{4}+20 x^{3}+150 x^{2}+500 x +625\right ) \left (x -2 \,{\mathrm e}^{x^{2}}\right )}\)	\(1812\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^9+100*x^8+996*x^7+4892*x^6+11380*x^5+6896*x^4-13516*x^3-12380*x^2+508*x)*exp(x^2)+x^8+25*x^7+250*x^
6+1254*x^5+3165*x^4+3225*x^3-5*x^2-5*x)*ln(2*x^2)^2+((-8*x^7-200*x^6-2000*x^5-9984*x^4-24760*x^3-23800*x^2+199
2*x-40)*exp(x^2)+4*x^8+100*x^7+1000*x^6+4992*x^5+12380*x^4+11900*x^3-996*x^2+20*x)*ln(2*x^2))/((4*x^6+100*x^5+
1000*x^4+5000*x^3+12500*x^2+12500*x)*exp(x^2)^2+(-4*x^7-100*x^6-1000*x^5-5000*x^4-12500*x^3-12500*x^2)*exp(x^2
)+x^8+25*x^7+250*x^6+1250*x^5+3125*x^4+3125*x^3),x,method=_RETURNVERBOSE)

[Out]

4*(x^6+20*x^5+150*x^4+498*x^3+605*x^2-50*x+1)/(x^4+20*x^3+150*x^2+500*x+625)/(x-2*exp(x^2))*ln(x)^2+2*(2*ln(2)
+300*x^4*ln(2)+40*x^5*ln(2)+2*x^6*ln(2)-100*x*ln(2)+1210*x^2*ln(2)+996*x^3*ln(2)-I*Pi*csgn(I*x)^2*csgn(I*x^2)+
2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-I*Pi*csgn(I*x^2)^3-605*I*Pi*x^2*csgn(I*x^2)^3+50*I*Pi*x*csgn(I*x^2)^3-I*Pi*x^6*
csgn(I*x^2)^3-20*I*Pi*x^5*csgn(I*x^2)^3-150*I*Pi*x^4*csgn(I*x^2)^3-498*I*Pi*x^3*csgn(I*x^2)^3-I*Pi*x^6*csgn(I*
x)^2*csgn(I*x^2)+2*I*Pi*x^6*csgn(I*x)*csgn(I*x^2)^2+50*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)-100*I*Pi*x*csgn(I*x)*csg
n(I*x^2)^2-605*I*Pi*x^2*csgn(I*x)^2*csgn(I*x^2)+1210*I*Pi*x^2*csgn(I*x)*csgn(I*x^2)^2-20*I*Pi*x^5*csgn(I*x)^2*
csgn(I*x^2)+40*I*Pi*x^5*csgn(I*x)*csgn(I*x^2)^2-150*I*Pi*x^4*csgn(I*x)^2*csgn(I*x^2)+300*I*Pi*x^4*csgn(I*x)*cs
gn(I*x^2)^2-498*I*Pi*x^3*csgn(I*x)^2*csgn(I*x^2)+996*I*Pi*x^3*csgn(I*x)*csgn(I*x^2)^2)/(5+x)/(x^3+15*x^2+75*x+
125)/(x-2*exp(x^2))*ln(x)+1/4*(4*x^6*ln(2)^2+4*ln(2)^2+80*x^5*ln(2)^2+600*x^4*ln(2)^2+1992*x^3*ln(2)^2-200*x*l
n(2)^2+2420*x^2*ln(2)^2+50*x*Pi^2*csgn(I*x)^4*csgn(I*x^2)^2-200*x*Pi^2*csgn(I*x)^3*csgn(I*x^2)^3+300*x*Pi^2*cs
gn(I*x)^2*csgn(I*x^2)^4-200*x*Pi^2*csgn(I*x)*csgn(I*x^2)^5-605*Pi^2*x^2*csgn(I*x)^4*csgn(I*x^2)^2+2420*Pi^2*x^
2*csgn(I*x)^3*csgn(I*x^2)^3-3630*Pi^2*x^2*csgn(I*x)^2*csgn(I*x^2)^4+2420*Pi^2*x^2*csgn(I*x)*csgn(I*x^2)^5-498*
Pi^2*x^3*csgn(I*x)^4*csgn(I*x^2)^2+1992*Pi^2*x^3*csgn(I*x)^3*csgn(I*x^2)^3-Pi^2*x^6*csgn(I*x)^4*csgn(I*x^2)^2+
4*Pi^2*x^6*csgn(I*x)^3*csgn(I*x^2)^3-6*Pi^2*x^6*csgn(I*x)^2*csgn(I*x^2)^4+4*Pi^2*x^6*csgn(I*x)*csgn(I*x^2)^5-4
*I*ln(2)*Pi*csgn(I*x^2)^3-Pi^2*x^6*csgn(I*x^2)^6-20*Pi^2*x^5*csgn(I*x)^4*csgn(I*x^2)^2+80*Pi^2*x^5*csgn(I*x)^3
*csgn(I*x^2)^3-120*Pi^2*x^5*csgn(I*x)^2*csgn(I*x^2)^4+80*Pi^2*x^5*csgn(I*x)*csgn(I*x^2)^5-20*Pi^2*x^5*csgn(I*x
^2)^6-150*Pi^2*x^4*csgn(I*x)^4*csgn(I*x^2)^2+600*Pi^2*x^4*csgn(I*x)^3*csgn(I*x^2)^3-900*Pi^2*x^4*csgn(I*x)^2*c
sgn(I*x^2)^4+600*Pi^2*x^4*csgn(I*x)*csgn(I*x^2)^5-150*Pi^2*x^4*csgn(I*x^2)^6+4*Pi^2*csgn(I*x^2)^5*csgn(I*x)-6*
Pi^2*csgn(I*x^2)^4*csgn(I*x)^2+4*Pi^2*csgn(I*x^2)^3*csgn(I*x)^3-Pi^2*csgn(I*x^2)^2*csgn(I*x)^4-605*Pi^2*x^2*cs
gn(I*x^2)^6-Pi^2*csgn(I*x^2)^6+50*x*Pi^2*csgn(I*x^2)^6-498*Pi^2*x^3*csgn(I*x^2)^6+1992*Pi^2*x^3*csgn(I*x)*csgn
(I*x^2)^5-1992*I*Pi*ln(2)*x^3*csgn(I*x^2)^3-2420*I*Pi*ln(2)*x^2*csgn(I*x^2)^3+200*I*Pi*ln(2)*x*csgn(I*x^2)^3-4
*I*Pi*ln(2)*x^6*csgn(I*x^2)^3-80*I*Pi*ln(2)*x^5*csgn(I*x^2)^3-600*I*Pi*ln(2)*x^4*csgn(I*x^2)^3-4*I*ln(2)*Pi*cs
gn(I*x)^2*csgn(I*x^2)+8*I*ln(2)*Pi*csgn(I*x)*csgn(I*x^2)^2-2988*Pi^2*x^3*csgn(I*x)^2*csgn(I*x^2)^4+200*I*Pi*ln
(2)*x*csgn(I*x)^2*csgn(I*x^2)-400*I*Pi*ln(2)*x*csgn(I*x)*csgn(I*x^2)^2-80*I*Pi*ln(2)*x^5*csgn(I*x)^2*csgn(I*x^
2)+160*I*Pi*ln(2)*x^5*csgn(I*x)*csgn(I*x^2)^2-600*I*Pi*ln(2)*x^4*csgn(I*x)^2*csgn(I*x^2)+1200*I*Pi*ln(2)*x^4*c
sgn(I*x)*csgn(I*x^2)^2-1992*I*Pi*ln(2)*x^3*csgn(I*x)^2*csgn(I*x^2)+3984*I*Pi*ln(2)*x^3*csgn(I*x)*csgn(I*x^2)^2
-2420*I*Pi*ln(2)*x^2*csgn(I*x)^2*csgn(I*x^2)+4840*I*Pi*ln(2)*x^2*csgn(I*x)*csgn(I*x^2)^2-4*I*Pi*ln(2)*x^6*csgn
(I*x)^2*csgn(I*x^2)+8*I*Pi*ln(2)*x^6*csgn(I*x)*csgn(I*x^2)^2)/(x^4+20*x^3+150*x^2+500*x+625)/(x-2*exp(x^2))

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maxima [B]  time = 0.55, size = 185, normalized size = 5.97 \begin {gather*} \frac {x^{6} \log \relax (2)^{2} + 20 \, x^{5} \log \relax (2)^{2} + 150 \, x^{4} \log \relax (2)^{2} + 498 \, x^{3} \log \relax (2)^{2} + 605 \, x^{2} \log \relax (2)^{2} - 50 \, x \log \relax (2)^{2} + 4 \, {\left (x^{6} + 20 \, x^{5} + 150 \, x^{4} + 498 \, x^{3} + 605 \, x^{2} - 50 \, x + 1\right )} \log \relax (x)^{2} + \log \relax (2)^{2} + 4 \, {\left (x^{6} \log \relax (2) + 20 \, x^{5} \log \relax (2) + 150 \, x^{4} \log \relax (2) + 498 \, x^{3} \log \relax (2) + 605 \, x^{2} \log \relax (2) - 50 \, x \log \relax (2) + \log \relax (2)\right )} \log \relax (x)}{x^{5} + 20 \, x^{4} + 150 \, x^{3} + 500 \, x^{2} - 2 \, {\left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + 625\right )} e^{\left (x^{2}\right )} + 625 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^9+100*x^8+996*x^7+4892*x^6+11380*x^5+6896*x^4-13516*x^3-12380*x^2+508*x)*exp(x^2)+x^8+25*x^7+
250*x^6+1254*x^5+3165*x^4+3225*x^3-5*x^2-5*x)*log(2*x^2)^2+((-8*x^7-200*x^6-2000*x^5-9984*x^4-24760*x^3-23800*
x^2+1992*x-40)*exp(x^2)+4*x^8+100*x^7+1000*x^6+4992*x^5+12380*x^4+11900*x^3-996*x^2+20*x)*log(2*x^2))/((4*x^6+
100*x^5+1000*x^4+5000*x^3+12500*x^2+12500*x)*exp(x^2)^2+(-4*x^7-100*x^6-1000*x^5-5000*x^4-12500*x^3-12500*x^2)
*exp(x^2)+x^8+25*x^7+250*x^6+1250*x^5+3125*x^4+3125*x^3),x, algorithm="maxima")

[Out]

(x^6*log(2)^2 + 20*x^5*log(2)^2 + 150*x^4*log(2)^2 + 498*x^3*log(2)^2 + 605*x^2*log(2)^2 - 50*x*log(2)^2 + 4*(
x^6 + 20*x^5 + 150*x^4 + 498*x^3 + 605*x^2 - 50*x + 1)*log(x)^2 + log(2)^2 + 4*(x^6*log(2) + 20*x^5*log(2) + 1
50*x^4*log(2) + 498*x^3*log(2) + 605*x^2*log(2) - 50*x*log(2) + log(2))*log(x))/(x^5 + 20*x^4 + 150*x^3 + 500*
x^2 - 2*(x^4 + 20*x^3 + 150*x^2 + 500*x + 625)*e^(x^2) + 625*x)

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mupad [B]  time = 5.71, size = 39, normalized size = 1.26 \begin {gather*} \frac {{\ln \left (2\,x^2\right )}^2\,{\left (x^3+10\,x^2+25\,x-1\right )}^2}{\left (x-2\,{\mathrm {e}}^{x^2}\right )\,{\left (x+5\right )}^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(2*x^2)^2*(exp(x^2)*(508*x - 12380*x^2 - 13516*x^3 + 6896*x^4 + 11380*x^5 + 4892*x^6 + 996*x^7 + 100*x
^8 + 4*x^9) - 5*x - 5*x^2 + 3225*x^3 + 3165*x^4 + 1254*x^5 + 250*x^6 + 25*x^7 + x^8) + log(2*x^2)*(20*x - exp(
x^2)*(23800*x^2 - 1992*x + 24760*x^3 + 9984*x^4 + 2000*x^5 + 200*x^6 + 8*x^7 + 40) - 996*x^2 + 11900*x^3 + 123
80*x^4 + 4992*x^5 + 1000*x^6 + 100*x^7 + 4*x^8))/(exp(2*x^2)*(12500*x + 12500*x^2 + 5000*x^3 + 1000*x^4 + 100*
x^5 + 4*x^6) - exp(x^2)*(12500*x^2 + 12500*x^3 + 5000*x^4 + 1000*x^5 + 100*x^6 + 4*x^7) + 3125*x^3 + 3125*x^4
+ 1250*x^5 + 250*x^6 + 25*x^7 + x^8),x)

[Out]

(log(2*x^2)^2*(25*x + 10*x^2 + x^3 - 1)^2)/((x - 2*exp(x^2))*(x + 5)^4)

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sympy [B]  time = 0.75, size = 133, normalized size = 4.29 \begin {gather*} \frac {- x^{6} \log {\left (2 x^{2} \right )}^{2} - 20 x^{5} \log {\left (2 x^{2} \right )}^{2} - 150 x^{4} \log {\left (2 x^{2} \right )}^{2} - 498 x^{3} \log {\left (2 x^{2} \right )}^{2} - 605 x^{2} \log {\left (2 x^{2} \right )}^{2} + 50 x \log {\left (2 x^{2} \right )}^{2} - \log {\left (2 x^{2} \right )}^{2}}{- x^{5} - 20 x^{4} - 150 x^{3} - 500 x^{2} - 625 x + \left (2 x^{4} + 40 x^{3} + 300 x^{2} + 1000 x + 1250\right ) e^{x^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x**9+100*x**8+996*x**7+4892*x**6+11380*x**5+6896*x**4-13516*x**3-12380*x**2+508*x)*exp(x**2)+x*
*8+25*x**7+250*x**6+1254*x**5+3165*x**4+3225*x**3-5*x**2-5*x)*ln(2*x**2)**2+((-8*x**7-200*x**6-2000*x**5-9984*
x**4-24760*x**3-23800*x**2+1992*x-40)*exp(x**2)+4*x**8+100*x**7+1000*x**6+4992*x**5+12380*x**4+11900*x**3-996*
x**2+20*x)*ln(2*x**2))/((4*x**6+100*x**5+1000*x**4+5000*x**3+12500*x**2+12500*x)*exp(x**2)**2+(-4*x**7-100*x**
6-1000*x**5-5000*x**4-12500*x**3-12500*x**2)*exp(x**2)+x**8+25*x**7+250*x**6+1250*x**5+3125*x**4+3125*x**3),x)

[Out]

(-x**6*log(2*x**2)**2 - 20*x**5*log(2*x**2)**2 - 150*x**4*log(2*x**2)**2 - 498*x**3*log(2*x**2)**2 - 605*x**2*
log(2*x**2)**2 + 50*x*log(2*x**2)**2 - log(2*x**2)**2)/(-x**5 - 20*x**4 - 150*x**3 - 500*x**2 - 625*x + (2*x**
4 + 40*x**3 + 300*x**2 + 1000*x + 1250)*exp(x**2))

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