3.3.53 \(\int \frac {409600+e^x (-384000-15360 x)+16384 x+e^{3 x} (-12500-16500 x-640 x^2)+e^{2 x} (120000+56000 x+49152 x^2+2048 x^3)+(2457600+e^x (-1536000-61440 x)+98304 x+e^{2 x} (240000+112000 x+100352 x^2+4096 x^3)) \log (\frac {25+x}{5})+(6758400+e^x (-2688000-107520 x)+270336 x+e^{2 x} (180000+84000 x+76800 x^2+3072 x^3)) \log ^2(\frac {25+x}{5})+(11264000+e^x (-2688000-107520 x)+450560 x+e^{2 x} (60000+28000 x+26112 x^2+1024 x^3)) \log ^3(\frac {25+x}{5})+(12672000+e^x (-1680000-67200 x)+506880 x+e^{2 x} (7500+3500 x+3328 x^2+128 x^3)) \log ^4(\frac {25+x}{5})+(10137600+e^x (-672000-26880 x)+405504 x) \log ^5(\frac {25+x}{5})+(5913600+e^x (-168000-6720 x)+236544 x) \log ^6(\frac {25+x}{5})+(2534400+e^x (-24000-960 x)+101376 x) \log ^7(\frac {25+x}{5})+(792000+e^x (-1500-60 x)+31680 x) \log ^8(\frac {25+x}{5})+(176000+7040 x) \log ^9(\frac {25+x}{5})+(26400+1056 x) \log ^{10}(\frac {25+x}{5})+(2400+96 x) \log ^{11}(\frac {25+x}{5})+(100+4 x) \log ^{12}(\frac {25+x}{5})}{102400+e^x (-96000-3840 x)+e^{3 x} (-3125-125 x)+4096 x+e^{2 x} (30000+1200 x)+(614400+e^x (-384000-15360 x)+24576 x+e^{2 x} (60000+2400 x)) \log (\frac {25+x}{5})+(1689600+e^x (-672000-26880 x)+67584 x+e^{2 x} (45000+1800 x)) \log ^2(\frac {25+x}{5})+(2816000+e^x (-672000-26880 x)+112640 x+e^{2 x} (15000+600 x)) \log ^3(\frac {25+x}{5})+(3168000+e^x (-420000-16800 x)+126720 x+e^{2 x} (1875+75 x)) \log ^4(\frac {25+x}{5})+(2534400+e^x (-168000-6720 x)+101376 x) \log ^5(\frac {25+x}{5})+(1478400+e^x (-42000-1680 x)+59136 x) \log ^6(\frac {25+x}{5})+(633600+e^x (-6000-240 x)+25344 x) \log ^7(\frac {25+x}{5})+(198000+e^x (-375-15 x)+7920 x) \log ^8(\frac {25+x}{5})+(44000+1760 x) \log ^9(\frac {25+x}{5})+(6600+264 x) \log ^{10}(\frac {25+x}{5})+(600+24 x) \log ^{11}(\frac {25+x}{5})+(25+x) \log ^{12}(\frac {25+x}{5})} \, dx\)

Optimal. Leaf size=31 \[ 4 \left (x+\frac {16 x^2}{\left (-5+e^{-x} \left (2+\log \left (5+\frac {x}{5}\right )\right )^4\right )^2}\right ) \]

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Rubi [F]  time = 180.01, 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[(409600 + E^x*(-384000 - 15360*x) + 16384*x + E^(3*x)*(-12500 - 16500*x - 640*x^2) + E^(2*x)*(120000 + 560
00*x + 49152*x^2 + 2048*x^3) + (2457600 + E^x*(-1536000 - 61440*x) + 98304*x + E^(2*x)*(240000 + 112000*x + 10
0352*x^2 + 4096*x^3))*Log[(25 + x)/5] + (6758400 + E^x*(-2688000 - 107520*x) + 270336*x + E^(2*x)*(180000 + 84
000*x + 76800*x^2 + 3072*x^3))*Log[(25 + x)/5]^2 + (11264000 + E^x*(-2688000 - 107520*x) + 450560*x + E^(2*x)*
(60000 + 28000*x + 26112*x^2 + 1024*x^3))*Log[(25 + x)/5]^3 + (12672000 + E^x*(-1680000 - 67200*x) + 506880*x
+ E^(2*x)*(7500 + 3500*x + 3328*x^2 + 128*x^3))*Log[(25 + x)/5]^4 + (10137600 + E^x*(-672000 - 26880*x) + 4055
04*x)*Log[(25 + x)/5]^5 + (5913600 + E^x*(-168000 - 6720*x) + 236544*x)*Log[(25 + x)/5]^6 + (2534400 + E^x*(-2
4000 - 960*x) + 101376*x)*Log[(25 + x)/5]^7 + (792000 + E^x*(-1500 - 60*x) + 31680*x)*Log[(25 + x)/5]^8 + (176
000 + 7040*x)*Log[(25 + x)/5]^9 + (26400 + 1056*x)*Log[(25 + x)/5]^10 + (2400 + 96*x)*Log[(25 + x)/5]^11 + (10
0 + 4*x)*Log[(25 + x)/5]^12)/(102400 + E^x*(-96000 - 3840*x) + E^(3*x)*(-3125 - 125*x) + 4096*x + E^(2*x)*(300
00 + 1200*x) + (614400 + E^x*(-384000 - 15360*x) + 24576*x + E^(2*x)*(60000 + 2400*x))*Log[(25 + x)/5] + (1689
600 + E^x*(-672000 - 26880*x) + 67584*x + E^(2*x)*(45000 + 1800*x))*Log[(25 + x)/5]^2 + (2816000 + E^x*(-67200
0 - 26880*x) + 112640*x + E^(2*x)*(15000 + 600*x))*Log[(25 + x)/5]^3 + (3168000 + E^x*(-420000 - 16800*x) + 12
6720*x + E^(2*x)*(1875 + 75*x))*Log[(25 + x)/5]^4 + (2534400 + E^x*(-168000 - 6720*x) + 101376*x)*Log[(25 + x)
/5]^5 + (1478400 + E^x*(-42000 - 1680*x) + 59136*x)*Log[(25 + x)/5]^6 + (633600 + E^x*(-6000 - 240*x) + 25344*
x)*Log[(25 + x)/5]^7 + (198000 + E^x*(-375 - 15*x) + 7920*x)*Log[(25 + x)/5]^8 + (44000 + 1760*x)*Log[(25 + x)
/5]^9 + (6600 + 264*x)*Log[(25 + x)/5]^10 + (600 + 24*x)*Log[(25 + x)/5]^11 + (25 + x)*Log[(25 + x)/5]^12),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 0.58, size = 69, normalized size = 2.23 \begin {gather*} -4 \left (-x-\frac {16 e^{2 x} x^2}{\left (16-5 e^x+32 \log \left (5+\frac {x}{5}\right )+24 \log ^2\left (5+\frac {x}{5}\right )+8 \log ^3\left (5+\frac {x}{5}\right )+\log ^4\left (5+\frac {x}{5}\right )\right )^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(409600 + E^x*(-384000 - 15360*x) + 16384*x + E^(3*x)*(-12500 - 16500*x - 640*x^2) + E^(2*x)*(120000
+ 56000*x + 49152*x^2 + 2048*x^3) + (2457600 + E^x*(-1536000 - 61440*x) + 98304*x + E^(2*x)*(240000 + 112000*
x + 100352*x^2 + 4096*x^3))*Log[(25 + x)/5] + (6758400 + E^x*(-2688000 - 107520*x) + 270336*x + E^(2*x)*(18000
0 + 84000*x + 76800*x^2 + 3072*x^3))*Log[(25 + x)/5]^2 + (11264000 + E^x*(-2688000 - 107520*x) + 450560*x + E^
(2*x)*(60000 + 28000*x + 26112*x^2 + 1024*x^3))*Log[(25 + x)/5]^3 + (12672000 + E^x*(-1680000 - 67200*x) + 506
880*x + E^(2*x)*(7500 + 3500*x + 3328*x^2 + 128*x^3))*Log[(25 + x)/5]^4 + (10137600 + E^x*(-672000 - 26880*x)
+ 405504*x)*Log[(25 + x)/5]^5 + (5913600 + E^x*(-168000 - 6720*x) + 236544*x)*Log[(25 + x)/5]^6 + (2534400 + E
^x*(-24000 - 960*x) + 101376*x)*Log[(25 + x)/5]^7 + (792000 + E^x*(-1500 - 60*x) + 31680*x)*Log[(25 + x)/5]^8
+ (176000 + 7040*x)*Log[(25 + x)/5]^9 + (26400 + 1056*x)*Log[(25 + x)/5]^10 + (2400 + 96*x)*Log[(25 + x)/5]^11
+ (100 + 4*x)*Log[(25 + x)/5]^12)/(102400 + E^x*(-96000 - 3840*x) + E^(3*x)*(-3125 - 125*x) + 4096*x + E^(2*x
)*(30000 + 1200*x) + (614400 + E^x*(-384000 - 15360*x) + 24576*x + E^(2*x)*(60000 + 2400*x))*Log[(25 + x)/5] +
(1689600 + E^x*(-672000 - 26880*x) + 67584*x + E^(2*x)*(45000 + 1800*x))*Log[(25 + x)/5]^2 + (2816000 + E^x*(
-672000 - 26880*x) + 112640*x + E^(2*x)*(15000 + 600*x))*Log[(25 + x)/5]^3 + (3168000 + E^x*(-420000 - 16800*x
) + 126720*x + E^(2*x)*(1875 + 75*x))*Log[(25 + x)/5]^4 + (2534400 + E^x*(-168000 - 6720*x) + 101376*x)*Log[(2
5 + x)/5]^5 + (1478400 + E^x*(-42000 - 1680*x) + 59136*x)*Log[(25 + x)/5]^6 + (633600 + E^x*(-6000 - 240*x) +
25344*x)*Log[(25 + x)/5]^7 + (198000 + E^x*(-375 - 15*x) + 7920*x)*Log[(25 + x)/5]^8 + (44000 + 1760*x)*Log[(2
5 + x)/5]^9 + (6600 + 264*x)*Log[(25 + x)/5]^10 + (600 + 24*x)*Log[(25 + x)/5]^11 + (25 + x)*Log[(25 + x)/5]^1
2),x]

[Out]

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

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fricas [B]  time = 1.01, size = 253, normalized size = 8.16 \begin {gather*} \frac {4 \, {\left (x \log \left (\frac {1}{5} \, x + 5\right )^{8} + 16 \, x \log \left (\frac {1}{5} \, x + 5\right )^{7} + 112 \, x \log \left (\frac {1}{5} \, x + 5\right )^{6} + 448 \, x \log \left (\frac {1}{5} \, x + 5\right )^{5} - 10 \, {\left (x e^{x} - 112 \, x\right )} \log \left (\frac {1}{5} \, x + 5\right )^{4} - 16 \, {\left (5 \, x e^{x} - 112 \, x\right )} \log \left (\frac {1}{5} \, x + 5\right )^{3} - 16 \, {\left (15 \, x e^{x} - 112 \, x\right )} \log \left (\frac {1}{5} \, x + 5\right )^{2} + {\left (16 \, x^{2} + 25 \, x\right )} e^{\left (2 \, x\right )} - 160 \, x e^{x} - 64 \, {\left (5 \, x e^{x} - 16 \, x\right )} \log \left (\frac {1}{5} \, x + 5\right ) + 256 \, x\right )}}{\log \left (\frac {1}{5} \, x + 5\right )^{8} + 16 \, \log \left (\frac {1}{5} \, x + 5\right )^{7} + 112 \, \log \left (\frac {1}{5} \, x + 5\right )^{6} - 10 \, {\left (e^{x} - 112\right )} \log \left (\frac {1}{5} \, x + 5\right )^{4} + 448 \, \log \left (\frac {1}{5} \, x + 5\right )^{5} - 16 \, {\left (5 \, e^{x} - 112\right )} \log \left (\frac {1}{5} \, x + 5\right )^{3} - 16 \, {\left (15 \, e^{x} - 112\right )} \log \left (\frac {1}{5} \, x + 5\right )^{2} - 64 \, {\left (5 \, e^{x} - 16\right )} \log \left (\frac {1}{5} \, x + 5\right ) + 25 \, e^{\left (2 \, x\right )} - 160 \, e^{x} + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+100)*log(1/5*x+5)^12+(96*x+2400)*log(1/5*x+5)^11+(1056*x+26400)*log(1/5*x+5)^10+(7040*x+176000
)*log(1/5*x+5)^9+((-60*x-1500)*exp(x)+31680*x+792000)*log(1/5*x+5)^8+((-960*x-24000)*exp(x)+101376*x+2534400)*
log(1/5*x+5)^7+((-6720*x-168000)*exp(x)+236544*x+5913600)*log(1/5*x+5)^6+((-26880*x-672000)*exp(x)+405504*x+10
137600)*log(1/5*x+5)^5+((128*x^3+3328*x^2+3500*x+7500)*exp(x)^2+(-67200*x-1680000)*exp(x)+506880*x+12672000)*l
og(1/5*x+5)^4+((1024*x^3+26112*x^2+28000*x+60000)*exp(x)^2+(-107520*x-2688000)*exp(x)+450560*x+11264000)*log(1
/5*x+5)^3+((3072*x^3+76800*x^2+84000*x+180000)*exp(x)^2+(-107520*x-2688000)*exp(x)+270336*x+6758400)*log(1/5*x
+5)^2+((4096*x^3+100352*x^2+112000*x+240000)*exp(x)^2+(-61440*x-1536000)*exp(x)+98304*x+2457600)*log(1/5*x+5)+
(-640*x^2-16500*x-12500)*exp(x)^3+(2048*x^3+49152*x^2+56000*x+120000)*exp(x)^2+(-15360*x-384000)*exp(x)+16384*
x+409600)/((x+25)*log(1/5*x+5)^12+(24*x+600)*log(1/5*x+5)^11+(264*x+6600)*log(1/5*x+5)^10+(1760*x+44000)*log(1
/5*x+5)^9+((-15*x-375)*exp(x)+7920*x+198000)*log(1/5*x+5)^8+((-240*x-6000)*exp(x)+25344*x+633600)*log(1/5*x+5)
^7+((-1680*x-42000)*exp(x)+59136*x+1478400)*log(1/5*x+5)^6+((-6720*x-168000)*exp(x)+101376*x+2534400)*log(1/5*
x+5)^5+((75*x+1875)*exp(x)^2+(-16800*x-420000)*exp(x)+126720*x+3168000)*log(1/5*x+5)^4+((600*x+15000)*exp(x)^2
+(-26880*x-672000)*exp(x)+112640*x+2816000)*log(1/5*x+5)^3+((1800*x+45000)*exp(x)^2+(-26880*x-672000)*exp(x)+6
7584*x+1689600)*log(1/5*x+5)^2+((2400*x+60000)*exp(x)^2+(-15360*x-384000)*exp(x)+24576*x+614400)*log(1/5*x+5)+
(-125*x-3125)*exp(x)^3+(1200*x+30000)*exp(x)^2+(-3840*x-96000)*exp(x)+4096*x+102400),x, algorithm="fricas")

[Out]

4*(x*log(1/5*x + 5)^8 + 16*x*log(1/5*x + 5)^7 + 112*x*log(1/5*x + 5)^6 + 448*x*log(1/5*x + 5)^5 - 10*(x*e^x -
112*x)*log(1/5*x + 5)^4 - 16*(5*x*e^x - 112*x)*log(1/5*x + 5)^3 - 16*(15*x*e^x - 112*x)*log(1/5*x + 5)^2 + (16
*x^2 + 25*x)*e^(2*x) - 160*x*e^x - 64*(5*x*e^x - 16*x)*log(1/5*x + 5) + 256*x)/(log(1/5*x + 5)^8 + 16*log(1/5*
x + 5)^7 + 112*log(1/5*x + 5)^6 - 10*(e^x - 112)*log(1/5*x + 5)^4 + 448*log(1/5*x + 5)^5 - 16*(5*e^x - 112)*lo
g(1/5*x + 5)^3 - 16*(15*e^x - 112)*log(1/5*x + 5)^2 - 64*(5*e^x - 16)*log(1/5*x + 5) + 25*e^(2*x) - 160*e^x +
256)

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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(((4*x+100)*log(1/5*x+5)^12+(96*x+2400)*log(1/5*x+5)^11+(1056*x+26400)*log(1/5*x+5)^10+(7040*x+176000
)*log(1/5*x+5)^9+((-60*x-1500)*exp(x)+31680*x+792000)*log(1/5*x+5)^8+((-960*x-24000)*exp(x)+101376*x+2534400)*
log(1/5*x+5)^7+((-6720*x-168000)*exp(x)+236544*x+5913600)*log(1/5*x+5)^6+((-26880*x-672000)*exp(x)+405504*x+10
137600)*log(1/5*x+5)^5+((128*x^3+3328*x^2+3500*x+7500)*exp(x)^2+(-67200*x-1680000)*exp(x)+506880*x+12672000)*l
og(1/5*x+5)^4+((1024*x^3+26112*x^2+28000*x+60000)*exp(x)^2+(-107520*x-2688000)*exp(x)+450560*x+11264000)*log(1
/5*x+5)^3+((3072*x^3+76800*x^2+84000*x+180000)*exp(x)^2+(-107520*x-2688000)*exp(x)+270336*x+6758400)*log(1/5*x
+5)^2+((4096*x^3+100352*x^2+112000*x+240000)*exp(x)^2+(-61440*x-1536000)*exp(x)+98304*x+2457600)*log(1/5*x+5)+
(-640*x^2-16500*x-12500)*exp(x)^3+(2048*x^3+49152*x^2+56000*x+120000)*exp(x)^2+(-15360*x-384000)*exp(x)+16384*
x+409600)/((x+25)*log(1/5*x+5)^12+(24*x+600)*log(1/5*x+5)^11+(264*x+6600)*log(1/5*x+5)^10+(1760*x+44000)*log(1
/5*x+5)^9+((-15*x-375)*exp(x)+7920*x+198000)*log(1/5*x+5)^8+((-240*x-6000)*exp(x)+25344*x+633600)*log(1/5*x+5)
^7+((-1680*x-42000)*exp(x)+59136*x+1478400)*log(1/5*x+5)^6+((-6720*x-168000)*exp(x)+101376*x+2534400)*log(1/5*
x+5)^5+((75*x+1875)*exp(x)^2+(-16800*x-420000)*exp(x)+126720*x+3168000)*log(1/5*x+5)^4+((600*x+15000)*exp(x)^2
+(-26880*x-672000)*exp(x)+112640*x+2816000)*log(1/5*x+5)^3+((1800*x+45000)*exp(x)^2+(-26880*x-672000)*exp(x)+6
7584*x+1689600)*log(1/5*x+5)^2+((2400*x+60000)*exp(x)^2+(-15360*x-384000)*exp(x)+24576*x+614400)*log(1/5*x+5)+
(-125*x-3125)*exp(x)^3+(1200*x+30000)*exp(x)^2+(-3840*x-96000)*exp(x)+4096*x+102400),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.15, size = 60, normalized size = 1.94

method	result	size
risch	\(4 x +\frac {64 x^{2} {\mathrm e}^{2 x}}{\left (-\ln \left (\frac {x}{5}+5\right )^{4}-8 \ln \left (\frac {x}{5}+5\right )^{3}-24 \ln \left (\frac {x}{5}+5\right )^{2}+5 \,{\mathrm e}^{x}-32 \ln \left (\frac {x}{5}+5\right )-16\right )^{2}}\)	\(60\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x+100)*ln(1/5*x+5)^12+(96*x+2400)*ln(1/5*x+5)^11+(1056*x+26400)*ln(1/5*x+5)^10+(7040*x+176000)*ln(1/5*
x+5)^9+((-60*x-1500)*exp(x)+31680*x+792000)*ln(1/5*x+5)^8+((-960*x-24000)*exp(x)+101376*x+2534400)*ln(1/5*x+5)
^7+((-6720*x-168000)*exp(x)+236544*x+5913600)*ln(1/5*x+5)^6+((-26880*x-672000)*exp(x)+405504*x+10137600)*ln(1/
5*x+5)^5+((128*x^3+3328*x^2+3500*x+7500)*exp(x)^2+(-67200*x-1680000)*exp(x)+506880*x+12672000)*ln(1/5*x+5)^4+(
(1024*x^3+26112*x^2+28000*x+60000)*exp(x)^2+(-107520*x-2688000)*exp(x)+450560*x+11264000)*ln(1/5*x+5)^3+((3072
*x^3+76800*x^2+84000*x+180000)*exp(x)^2+(-107520*x-2688000)*exp(x)+270336*x+6758400)*ln(1/5*x+5)^2+((4096*x^3+
100352*x^2+112000*x+240000)*exp(x)^2+(-61440*x-1536000)*exp(x)+98304*x+2457600)*ln(1/5*x+5)+(-640*x^2-16500*x-
12500)*exp(x)^3+(2048*x^3+49152*x^2+56000*x+120000)*exp(x)^2+(-15360*x-384000)*exp(x)+16384*x+409600)/((x+25)*
ln(1/5*x+5)^12+(24*x+600)*ln(1/5*x+5)^11+(264*x+6600)*ln(1/5*x+5)^10+(1760*x+44000)*ln(1/5*x+5)^9+((-15*x-375)
*exp(x)+7920*x+198000)*ln(1/5*x+5)^8+((-240*x-6000)*exp(x)+25344*x+633600)*ln(1/5*x+5)^7+((-1680*x-42000)*exp(
x)+59136*x+1478400)*ln(1/5*x+5)^6+((-6720*x-168000)*exp(x)+101376*x+2534400)*ln(1/5*x+5)^5+((75*x+1875)*exp(x)
^2+(-16800*x-420000)*exp(x)+126720*x+3168000)*ln(1/5*x+5)^4+((600*x+15000)*exp(x)^2+(-26880*x-672000)*exp(x)+1
12640*x+2816000)*ln(1/5*x+5)^3+((1800*x+45000)*exp(x)^2+(-26880*x-672000)*exp(x)+67584*x+1689600)*ln(1/5*x+5)^
2+((2400*x+60000)*exp(x)^2+(-15360*x-384000)*exp(x)+24576*x+614400)*ln(1/5*x+5)+(-125*x-3125)*exp(x)^3+(1200*x
+30000)*exp(x)^2+(-3840*x-96000)*exp(x)+4096*x+102400),x,method=_RETURNVERBOSE)

[Out]

4*x+64*x^2*exp(2*x)/(-ln(1/5*x+5)^4-8*ln(1/5*x+5)^3-24*ln(1/5*x+5)^2+5*exp(x)-32*ln(1/5*x+5)-16)^2

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maxima [B]  time = 2.68, size = 726, normalized size = 23.42 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+100)*log(1/5*x+5)^12+(96*x+2400)*log(1/5*x+5)^11+(1056*x+26400)*log(1/5*x+5)^10+(7040*x+176000
)*log(1/5*x+5)^9+((-60*x-1500)*exp(x)+31680*x+792000)*log(1/5*x+5)^8+((-960*x-24000)*exp(x)+101376*x+2534400)*
log(1/5*x+5)^7+((-6720*x-168000)*exp(x)+236544*x+5913600)*log(1/5*x+5)^6+((-26880*x-672000)*exp(x)+405504*x+10
137600)*log(1/5*x+5)^5+((128*x^3+3328*x^2+3500*x+7500)*exp(x)^2+(-67200*x-1680000)*exp(x)+506880*x+12672000)*l
og(1/5*x+5)^4+((1024*x^3+26112*x^2+28000*x+60000)*exp(x)^2+(-107520*x-2688000)*exp(x)+450560*x+11264000)*log(1
/5*x+5)^3+((3072*x^3+76800*x^2+84000*x+180000)*exp(x)^2+(-107520*x-2688000)*exp(x)+270336*x+6758400)*log(1/5*x
+5)^2+((4096*x^3+100352*x^2+112000*x+240000)*exp(x)^2+(-61440*x-1536000)*exp(x)+98304*x+2457600)*log(1/5*x+5)+
(-640*x^2-16500*x-12500)*exp(x)^3+(2048*x^3+49152*x^2+56000*x+120000)*exp(x)^2+(-15360*x-384000)*exp(x)+16384*
x+409600)/((x+25)*log(1/5*x+5)^12+(24*x+600)*log(1/5*x+5)^11+(264*x+6600)*log(1/5*x+5)^10+(1760*x+44000)*log(1
/5*x+5)^9+((-15*x-375)*exp(x)+7920*x+198000)*log(1/5*x+5)^8+((-240*x-6000)*exp(x)+25344*x+633600)*log(1/5*x+5)
^7+((-1680*x-42000)*exp(x)+59136*x+1478400)*log(1/5*x+5)^6+((-6720*x-168000)*exp(x)+101376*x+2534400)*log(1/5*
x+5)^5+((75*x+1875)*exp(x)^2+(-16800*x-420000)*exp(x)+126720*x+3168000)*log(1/5*x+5)^4+((600*x+15000)*exp(x)^2
+(-26880*x-672000)*exp(x)+112640*x+2816000)*log(1/5*x+5)^3+((1800*x+45000)*exp(x)^2+(-26880*x-672000)*exp(x)+6
7584*x+1689600)*log(1/5*x+5)^2+((2400*x+60000)*exp(x)^2+(-15360*x-384000)*exp(x)+24576*x+614400)*log(1/5*x+5)+
(-125*x-3125)*exp(x)^3+(1200*x+30000)*exp(x)^2+(-3840*x-96000)*exp(x)+4096*x+102400),x, algorithm="maxima")

[Out]

-4*(8*x*(log(5) - 2)*log(x + 25)^7 - x*log(x + 25)^8 - 28*(log(5)^2 - 4*log(5) + 4)*x*log(x + 25)^6 + 56*(log(
5)^3 - 6*log(5)^2 + 12*log(5) - 8)*x*log(x + 25)^5 - 10*(7*(log(5)^4 - 8*log(5)^3 + 24*log(5)^2 - 32*log(5) +
16)*x - x*e^x)*log(x + 25)^4 - 8*(5*x*(log(5) - 2)*e^x - 7*(log(5)^5 - 10*log(5)^4 + 40*log(5)^3 - 80*log(5)^2
+ 80*log(5) - 32)*x)*log(x + 25)^3 + 10*(log(5)^4 - 8*log(5)^3 + 24*log(5)^2 - 32*log(5) + 16)*x*e^x + 4*(15*
(log(5)^2 - 4*log(5) + 4)*x*e^x - 7*(log(5)^6 - 12*log(5)^5 + 60*log(5)^4 - 160*log(5)^3 + 240*log(5)^2 - 192*
log(5) + 64)*x)*log(x + 25)^2 - (log(5)^8 - 16*log(5)^7 + 112*log(5)^6 - 448*log(5)^5 + 1120*log(5)^4 - 1792*l
og(5)^3 + 1792*log(5)^2 - 1024*log(5) + 256)*x - (16*x^2 + 25*x)*e^(2*x) - 8*(5*(log(5)^3 - 6*log(5)^2 + 12*lo
g(5) - 8)*x*e^x - (log(5)^7 - 14*log(5)^6 + 84*log(5)^5 - 280*log(5)^4 + 560*log(5)^3 - 672*log(5)^2 + 448*log
(5) - 128)*x)*log(x + 25))/(log(5)^8 - 8*(log(5) - 2)*log(x + 25)^7 + log(x + 25)^8 - 16*log(5)^7 + 28*(log(5)
^2 - 4*log(5) + 4)*log(x + 25)^6 + 112*log(5)^6 - 56*(log(5)^3 - 6*log(5)^2 + 12*log(5) - 8)*log(x + 25)^5 - 4
48*log(5)^5 + 10*(7*log(5)^4 - 56*log(5)^3 + 168*log(5)^2 - e^x - 224*log(5) + 112)*log(x + 25)^4 + 1120*log(5
)^4 - 8*(7*log(5)^5 - 70*log(5)^4 + 280*log(5)^3 - 5*(log(5) - 2)*e^x - 560*log(5)^2 + 560*log(5) - 224)*log(x
+ 25)^3 - 1792*log(5)^3 + 4*(7*log(5)^6 - 84*log(5)^5 + 420*log(5)^4 - 1120*log(5)^3 - 15*(log(5)^2 - 4*log(5
) + 4)*e^x + 1680*log(5)^2 - 1344*log(5) + 448)*log(x + 25)^2 - 10*(log(5)^4 - 8*log(5)^3 + 24*log(5)^2 - 32*l
og(5) + 16)*e^x + 1792*log(5)^2 - 8*(log(5)^7 - 14*log(5)^6 + 84*log(5)^5 - 280*log(5)^4 + 560*log(5)^3 - 5*(l
og(5)^3 - 6*log(5)^2 + 12*log(5) - 8)*e^x - 672*log(5)^2 + 448*log(5) - 128)*log(x + 25) + 25*e^(2*x) - 1024*l
og(5) + 256)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16384*x - exp(3*x)*(16500*x + 640*x^2 + 12500) + log(x/5 + 5)^8*(31680*x - exp(x)*(60*x + 1500) + 792000)
+ log(x/5 + 5)^7*(101376*x - exp(x)*(960*x + 24000) + 2534400) + log(x/5 + 5)^6*(236544*x - exp(x)*(6720*x +
168000) + 5913600) + log(x/5 + 5)^5*(405504*x - exp(x)*(26880*x + 672000) + 10137600) + exp(2*x)*(56000*x + 49
152*x^2 + 2048*x^3 + 120000) + log(x/5 + 5)^2*(270336*x + exp(2*x)*(84000*x + 76800*x^2 + 3072*x^3 + 180000) -
exp(x)*(107520*x + 2688000) + 6758400) + log(x/5 + 5)^3*(450560*x + exp(2*x)*(28000*x + 26112*x^2 + 1024*x^3
+ 60000) - exp(x)*(107520*x + 2688000) + 11264000) + log(x/5 + 5)^4*(506880*x + exp(2*x)*(3500*x + 3328*x^2 +
128*x^3 + 7500) - exp(x)*(67200*x + 1680000) + 12672000) - exp(x)*(15360*x + 384000) + log(x/5 + 5)^12*(4*x +
100) + log(x/5 + 5)^11*(96*x + 2400) + log(x/5 + 5)^10*(1056*x + 26400) + log(x/5 + 5)^9*(7040*x + 176000) + l
og(x/5 + 5)*(98304*x + exp(2*x)*(112000*x + 100352*x^2 + 4096*x^3 + 240000) - exp(x)*(61440*x + 1536000) + 245
7600) + 409600)/(4096*x + log(x/5 + 5)^8*(7920*x - exp(x)*(15*x + 375) + 198000) + log(x/5 + 5)^7*(25344*x - e
xp(x)*(240*x + 6000) + 633600) + log(x/5 + 5)^6*(59136*x - exp(x)*(1680*x + 42000) + 1478400) + log(x/5 + 5)^5
*(101376*x - exp(x)*(6720*x + 168000) + 2534400) + log(x/5 + 5)^12*(x + 25) - exp(x)*(3840*x + 96000) + log(x/
5 + 5)*(24576*x - exp(x)*(15360*x + 384000) + exp(2*x)*(2400*x + 60000) + 614400) + log(x/5 + 5)^11*(24*x + 60
0) + log(x/5 + 5)^10*(264*x + 6600) + log(x/5 + 5)^9*(1760*x + 44000) - exp(3*x)*(125*x + 3125) + exp(2*x)*(12
00*x + 30000) + log(x/5 + 5)^2*(67584*x - exp(x)*(26880*x + 672000) + exp(2*x)*(1800*x + 45000) + 1689600) + l
og(x/5 + 5)^3*(112640*x - exp(x)*(26880*x + 672000) + exp(2*x)*(600*x + 15000) + 2816000) + log(x/5 + 5)^4*(12
6720*x - exp(x)*(16800*x + 420000) + exp(2*x)*(75*x + 1875) + 3168000) + 102400),x)

[Out]

int((16384*x - exp(3*x)*(16500*x + 640*x^2 + 12500) + log(x/5 + 5)^8*(31680*x - exp(x)*(60*x + 1500) + 792000)
+ log(x/5 + 5)^7*(101376*x - exp(x)*(960*x + 24000) + 2534400) + log(x/5 + 5)^6*(236544*x - exp(x)*(6720*x +
168000) + 5913600) + log(x/5 + 5)^5*(405504*x - exp(x)*(26880*x + 672000) + 10137600) + exp(2*x)*(56000*x + 49
152*x^2 + 2048*x^3 + 120000) + log(x/5 + 5)^2*(270336*x + exp(2*x)*(84000*x + 76800*x^2 + 3072*x^3 + 180000) -
exp(x)*(107520*x + 2688000) + 6758400) + log(x/5 + 5)^3*(450560*x + exp(2*x)*(28000*x + 26112*x^2 + 1024*x^3
+ 60000) - exp(x)*(107520*x + 2688000) + 11264000) + log(x/5 + 5)^4*(506880*x + exp(2*x)*(3500*x + 3328*x^2 +
128*x^3 + 7500) - exp(x)*(67200*x + 1680000) + 12672000) - exp(x)*(15360*x + 384000) + log(x/5 + 5)^12*(4*x +
100) + log(x/5 + 5)^11*(96*x + 2400) + log(x/5 + 5)^10*(1056*x + 26400) + log(x/5 + 5)^9*(7040*x + 176000) + l
og(x/5 + 5)*(98304*x + exp(2*x)*(112000*x + 100352*x^2 + 4096*x^3 + 240000) - exp(x)*(61440*x + 1536000) + 245
7600) + 409600)/(4096*x + log(x/5 + 5)^8*(7920*x - exp(x)*(15*x + 375) + 198000) + log(x/5 + 5)^7*(25344*x - e
xp(x)*(240*x + 6000) + 633600) + log(x/5 + 5)^6*(59136*x - exp(x)*(1680*x + 42000) + 1478400) + log(x/5 + 5)^5
*(101376*x - exp(x)*(6720*x + 168000) + 2534400) + log(x/5 + 5)^12*(x + 25) - exp(x)*(3840*x + 96000) + log(x/
5 + 5)*(24576*x - exp(x)*(15360*x + 384000) + exp(2*x)*(2400*x + 60000) + 614400) + log(x/5 + 5)^11*(24*x + 60
0) + log(x/5 + 5)^10*(264*x + 6600) + log(x/5 + 5)^9*(1760*x + 44000) - exp(3*x)*(125*x + 3125) + exp(2*x)*(12
00*x + 30000) + log(x/5 + 5)^2*(67584*x - exp(x)*(26880*x + 672000) + exp(2*x)*(1800*x + 45000) + 1689600) + l
og(x/5 + 5)^3*(112640*x - exp(x)*(26880*x + 672000) + exp(2*x)*(600*x + 15000) + 2816000) + log(x/5 + 5)^4*(12
6720*x - exp(x)*(16800*x + 420000) + exp(2*x)*(75*x + 1875) + 3168000) + 102400), x)

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sympy [B]  time = 1.57, size = 316, normalized size = 10.19 \begin {gather*} \frac {64 x^{2}}{25} + 4 x + \frac {- 64 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{8} - 1024 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{7} - 7168 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{6} - 28672 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{5} - 71680 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{4} - 114688 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{3} - 114688 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{2} - 65536 x^{2} \log {\left (\frac {x}{5} + 5 \right )} - 16384 x^{2} + \left (640 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{4} + 5120 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{3} + 15360 x^{2} \log {\left (\frac {x}{5} + 5 \right )}^{2} + 20480 x^{2} \log {\left (\frac {x}{5} + 5 \right )} + 10240 x^{2}\right ) e^{x}}{\left (- 250 \log {\left (\frac {x}{5} + 5 \right )}^{4} - 2000 \log {\left (\frac {x}{5} + 5 \right )}^{3} - 6000 \log {\left (\frac {x}{5} + 5 \right )}^{2} - 8000 \log {\left (\frac {x}{5} + 5 \right )} - 4000\right ) e^{x} + 625 e^{2 x} + 25 \log {\left (\frac {x}{5} + 5 \right )}^{8} + 400 \log {\left (\frac {x}{5} + 5 \right )}^{7} + 2800 \log {\left (\frac {x}{5} + 5 \right )}^{6} + 11200 \log {\left (\frac {x}{5} + 5 \right )}^{5} + 28000 \log {\left (\frac {x}{5} + 5 \right )}^{4} + 44800 \log {\left (\frac {x}{5} + 5 \right )}^{3} + 44800 \log {\left (\frac {x}{5} + 5 \right )}^{2} + 25600 \log {\left (\frac {x}{5} + 5 \right )} + 6400} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+100)*ln(1/5*x+5)**12+(96*x+2400)*ln(1/5*x+5)**11+(1056*x+26400)*ln(1/5*x+5)**10+(7040*x+176000
)*ln(1/5*x+5)**9+((-60*x-1500)*exp(x)+31680*x+792000)*ln(1/5*x+5)**8+((-960*x-24000)*exp(x)+101376*x+2534400)*
ln(1/5*x+5)**7+((-6720*x-168000)*exp(x)+236544*x+5913600)*ln(1/5*x+5)**6+((-26880*x-672000)*exp(x)+405504*x+10
137600)*ln(1/5*x+5)**5+((128*x**3+3328*x**2+3500*x+7500)*exp(x)**2+(-67200*x-1680000)*exp(x)+506880*x+12672000
)*ln(1/5*x+5)**4+((1024*x**3+26112*x**2+28000*x+60000)*exp(x)**2+(-107520*x-2688000)*exp(x)+450560*x+11264000)
*ln(1/5*x+5)**3+((3072*x**3+76800*x**2+84000*x+180000)*exp(x)**2+(-107520*x-2688000)*exp(x)+270336*x+6758400)*
ln(1/5*x+5)**2+((4096*x**3+100352*x**2+112000*x+240000)*exp(x)**2+(-61440*x-1536000)*exp(x)+98304*x+2457600)*l
n(1/5*x+5)+(-640*x**2-16500*x-12500)*exp(x)**3+(2048*x**3+49152*x**2+56000*x+120000)*exp(x)**2+(-15360*x-38400
0)*exp(x)+16384*x+409600)/((x+25)*ln(1/5*x+5)**12+(24*x+600)*ln(1/5*x+5)**11+(264*x+6600)*ln(1/5*x+5)**10+(176
0*x+44000)*ln(1/5*x+5)**9+((-15*x-375)*exp(x)+7920*x+198000)*ln(1/5*x+5)**8+((-240*x-6000)*exp(x)+25344*x+6336
00)*ln(1/5*x+5)**7+((-1680*x-42000)*exp(x)+59136*x+1478400)*ln(1/5*x+5)**6+((-6720*x-168000)*exp(x)+101376*x+2
534400)*ln(1/5*x+5)**5+((75*x+1875)*exp(x)**2+(-16800*x-420000)*exp(x)+126720*x+3168000)*ln(1/5*x+5)**4+((600*
x+15000)*exp(x)**2+(-26880*x-672000)*exp(x)+112640*x+2816000)*ln(1/5*x+5)**3+((1800*x+45000)*exp(x)**2+(-26880
*x-672000)*exp(x)+67584*x+1689600)*ln(1/5*x+5)**2+((2400*x+60000)*exp(x)**2+(-15360*x-384000)*exp(x)+24576*x+6
14400)*ln(1/5*x+5)+(-125*x-3125)*exp(x)**3+(1200*x+30000)*exp(x)**2+(-3840*x-96000)*exp(x)+4096*x+102400),x)

[Out]

64*x**2/25 + 4*x + (-64*x**2*log(x/5 + 5)**8 - 1024*x**2*log(x/5 + 5)**7 - 7168*x**2*log(x/5 + 5)**6 - 28672*x
**2*log(x/5 + 5)**5 - 71680*x**2*log(x/5 + 5)**4 - 114688*x**2*log(x/5 + 5)**3 - 114688*x**2*log(x/5 + 5)**2 -
65536*x**2*log(x/5 + 5) - 16384*x**2 + (640*x**2*log(x/5 + 5)**4 + 5120*x**2*log(x/5 + 5)**3 + 15360*x**2*log
(x/5 + 5)**2 + 20480*x**2*log(x/5 + 5) + 10240*x**2)*exp(x))/((-250*log(x/5 + 5)**4 - 2000*log(x/5 + 5)**3 - 6
000*log(x/5 + 5)**2 - 8000*log(x/5 + 5) - 4000)*exp(x) + 625*exp(2*x) + 25*log(x/5 + 5)**8 + 400*log(x/5 + 5)*
*7 + 2800*log(x/5 + 5)**6 + 11200*log(x/5 + 5)**5 + 28000*log(x/5 + 5)**4 + 44800*log(x/5 + 5)**3 + 44800*log(
x/5 + 5)**2 + 25600*log(x/5 + 5) + 6400)

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