3.37.64 \(\int \frac {-4398046511104 e^{-20460-20 x}-17179869184 e^{-15345-15 x} x-25165824 e^{-10230-10 x} x^2-16384 e^{-5115-5 x} x^3-4 x^4+(-21990232555520 e^{-20460-20 x} x+4 x^4+1073741824 e^{-15345-15 x} (4 x-60 x^2)+1048576 e^{-10230-10 x} (12 x^2-60 x^3)+1024 e^{-5115-5 x} (12 x^3-20 x^4)) \log (x)}{x \log ^5(x)} \, dx\)

Optimal. Leaf size=20 \[ \frac {\left (e^{5 (-1023-x+\log (4))}+x\right )^4}{\log ^4(x)} \]

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Rubi [F]  time = 188.08, 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[(-4398046511104*E^(-20460 - 20*x) - 17179869184*E^(-15345 - 15*x)*x - 25165824*E^(-10230 - 10*x)*x^2 - 163
84*E^(-5115 - 5*x)*x^3 - 4*x^4 + (-21990232555520*E^(-20460 - 20*x)*x + 4*x^4 + 1073741824*E^(-15345 - 15*x)*(
4*x - 60*x^2) + 1048576*E^(-10230 - 10*x)*(12*x^2 - 60*x^3) + 1024*E^(-5115 - 5*x)*(12*x^3 - 20*x^4))*Log[x])/
(x*Log[x]^5),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 178.37, size = 23, normalized size = 1.15 \begin {gather*} \frac {\left (1024 e^{-5 x}+e^{5115} x\right )^4}{e^{20460} \log ^4(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4398046511104*E^(-20460 - 20*x) - 17179869184*E^(-15345 - 15*x)*x - 25165824*E^(-10230 - 10*x)*x^2
- 16384*E^(-5115 - 5*x)*x^3 - 4*x^4 + (-21990232555520*E^(-20460 - 20*x)*x + 4*x^4 + 1073741824*E^(-15345 - 1
5*x)*(4*x - 60*x^2) + 1048576*E^(-10230 - 10*x)*(12*x^2 - 60*x^3) + 1024*E^(-5115 - 5*x)*(12*x^3 - 20*x^4))*Lo
g[x])/(x*Log[x]^5),x]

[Out]

(1024/E^(5*x) + E^5115*x)^4/(E^20460*Log[x]^4)

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fricas [B]  time = 0.88, size = 62, normalized size = 3.10 \begin {gather*} \frac {x^{4} + 4 \, x^{3} e^{\left (-5 \, x + 10 \, \log \relax (2) - 5115\right )} + 6 \, x^{2} e^{\left (-10 \, x + 20 \, \log \relax (2) - 10230\right )} + 4 \, x e^{\left (-15 \, x + 30 \, \log \relax (2) - 15345\right )} + e^{\left (-20 \, x + 40 \, \log \relax (2) - 20460\right )}}{\log \relax (x)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*x*exp(10*log(2)-5*x-5115)^4+(-60*x^2+4*x)*exp(10*log(2)-5*x-5115)^3+(-60*x^3+12*x^2)*exp(10*lo
g(2)-5*x-5115)^2+(-20*x^4+12*x^3)*exp(10*log(2)-5*x-5115)+4*x^4)*log(x)-4*exp(10*log(2)-5*x-5115)^4-16*x*exp(1
0*log(2)-5*x-5115)^3-24*x^2*exp(10*log(2)-5*x-5115)^2-16*x^3*exp(10*log(2)-5*x-5115)-4*x^4)/x/log(x)^5,x, algo
rithm="fricas")

[Out]

(x^4 + 4*x^3*e^(-5*x + 10*log(2) - 5115) + 6*x^2*e^(-10*x + 20*log(2) - 10230) + 4*x*e^(-15*x + 30*log(2) - 15
345) + e^(-20*x + 40*log(2) - 20460))/log(x)^4

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giac [B]  time = 0.94, size = 53, normalized size = 2.65 \begin {gather*} \frac {{\left (x^{4} e^{51150} + 4096 \, x^{3} e^{\left (-5 \, x + 46035\right )} + 6291456 \, x^{2} e^{\left (-10 \, x + 40920\right )} + 4294967296 \, x e^{\left (-15 \, x + 35805\right )} + 1099511627776 \, e^{\left (-20 \, x + 30690\right )}\right )} e^{\left (-51150\right )}}{\log \relax (x)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*x*exp(10*log(2)-5*x-5115)^4+(-60*x^2+4*x)*exp(10*log(2)-5*x-5115)^3+(-60*x^3+12*x^2)*exp(10*lo
g(2)-5*x-5115)^2+(-20*x^4+12*x^3)*exp(10*log(2)-5*x-5115)+4*x^4)*log(x)-4*exp(10*log(2)-5*x-5115)^4-16*x*exp(1
0*log(2)-5*x-5115)^3-24*x^2*exp(10*log(2)-5*x-5115)^2-16*x^3*exp(10*log(2)-5*x-5115)-4*x^4)/x/log(x)^5,x, algo
rithm="giac")

[Out]

(x^4*e^51150 + 4096*x^3*e^(-5*x + 46035) + 6291456*x^2*e^(-10*x + 40920) + 4294967296*x*e^(-15*x + 35805) + 10
99511627776*e^(-20*x + 30690))*e^(-51150)/log(x)^4

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maple [B]  time = 0.06, size = 49, normalized size = 2.45

method	result	size
risch	\(\frac {x^{4}+4096 x^{3} {\mathrm e}^{-5115-5 x}+6291456 x^{2} {\mathrm e}^{-10230-10 x}[phone] x \,{\mathrm e}^{-15345-15 x}[phone] \,{\mathrm e}^{-20460-20 x}}{\ln \relax (x )^{4}}\)	\(49\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-20*x*exp(10*ln(2)-5*x-5115)^4+(-60*x^2+4*x)*exp(10*ln(2)-5*x-5115)^3+(-60*x^3+12*x^2)*exp(10*ln(2)-5*x-
5115)^2+(-20*x^4+12*x^3)*exp(10*ln(2)-5*x-5115)+4*x^4)*ln(x)-4*exp(10*ln(2)-5*x-5115)^4-16*x*exp(10*ln(2)-5*x-
5115)^3-24*x^2*exp(10*ln(2)-5*x-5115)^2-16*x^3*exp(10*ln(2)-5*x-5115)-4*x^4)/x/ln(x)^5,x,method=_RETURNVERBOSE
)

[Out]

(x^4+4096*x^3*exp(-5115-5*x)+6291456*x^2*exp(-10230-10*x)[phone]*x*exp(-15345-15*x)[phone]*exp(-204
60-20*x))/ln(x)^4

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {4 \, {\left (8 \, x^{4} e^{20460} \log \relax (x)^{3} + 2 \, x^{4} e^{20460} \log \relax (x)^{2} + x^{4} e^{20460} \log \relax (x) - 3072 \, x^{3} e^{\left (-5 \, x + 15345\right )} - 4718592 \, x^{2} e^{\left (-10 \, x + 10230\right )} - 3221225472 \, x e^{\left (-15 \, x + 5115\right )} - 824633720832 \, e^{\left (-20 \, x\right )}\right )} e^{\left (-20460\right )}}{3 \, \log \relax (x)^{4}} + 1024 \, \Gamma \left (-4, -4 \, \log \relax (x)\right ) + \frac {128}{3} \, \int \frac {x^{3}}{\log \relax (x)}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*x*exp(10*log(2)-5*x-5115)^4+(-60*x^2+4*x)*exp(10*log(2)-5*x-5115)^3+(-60*x^3+12*x^2)*exp(10*lo
g(2)-5*x-5115)^2+(-20*x^4+12*x^3)*exp(10*log(2)-5*x-5115)+4*x^4)*log(x)-4*exp(10*log(2)-5*x-5115)^4-16*x*exp(1
0*log(2)-5*x-5115)^3-24*x^2*exp(10*log(2)-5*x-5115)^2-16*x^3*exp(10*log(2)-5*x-5115)-4*x^4)/x/log(x)^5,x, algo
rithm="maxima")

[Out]

-4/3*(8*x^4*e^20460*log(x)^3 + 2*x^4*e^20460*log(x)^2 + x^4*e^20460*log(x) - 3072*x^3*e^(-5*x + 15345) - 47185
92*x^2*e^(-10*x + 10230) - 3221225472*x*e^(-15*x + 5115) - 824633720832*e^(-20*x))*e^(-20460)/log(x)^4 + 1024*
gamma(-4, -4*log(x)) + 128/3*integrate(x^3/log(x), x)

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mupad [B]  time = 2.32, size = 64, normalized size = 3.20 \begin {gather*} \frac {1099511627776\,{\mathrm {e}}^{-20\,x-20460}}{{\ln \relax (x)}^4}+\frac {x^4}{{\ln \relax (x)}^4}+\frac {4096\,x^3\,{\mathrm {e}}^{-5\,x-5115}}{{\ln \relax (x)}^4}+\frac {6291456\,x^2\,{\mathrm {e}}^{-10\,x-10230}}{{\ln \relax (x)}^4}+\frac {4294967296\,x\,{\mathrm {e}}^{-15\,x-15345}}{{\ln \relax (x)}^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*exp(40*log(2) - 20*x - 20460) + 16*x*exp(30*log(2) - 15*x - 15345) - log(x)*(exp(30*log(2) - 15*x - 15
345)*(4*x - 60*x^2) - 20*x*exp(40*log(2) - 20*x - 20460) + exp(10*log(2) - 5*x - 5115)*(12*x^3 - 20*x^4) + exp
(20*log(2) - 10*x - 10230)*(12*x^2 - 60*x^3) + 4*x^4) + 16*x^3*exp(10*log(2) - 5*x - 5115) + 24*x^2*exp(20*log
(2) - 10*x - 10230) + 4*x^4)/(x*log(x)^5),x)

[Out]

(1099511627776*exp(- 20*x - 20460))/log(x)^4 + x^4/log(x)^4 + (4096*x^3*exp(- 5*x - 5115))/log(x)^4 + (6291456
*x^2*exp(- 10*x - 10230))/log(x)^4 + (4294967296*x*exp(- 15*x - 15345))/log(x)^4

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sympy [B]  time = 0.46, size = 82, normalized size = 4.10 \begin {gather*} \frac {x^{4}}{\log {\relax (x )}^{4}} + \frac {4096 x^{3} e^{- 5 x - 5115} \log {\relax (x )}^{12} + 6291456 x^{2} e^{- 10 x - 10230} \log {\relax (x )}^{12} + 4294967296 x e^{- 15 x - 15345} \log {\relax (x )}^{12} + 1099511627776 e^{- 20 x - 20460} \log {\relax (x )}^{12}}{\log {\relax (x )}^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*x*exp(10*ln(2)-5*x-5115)**4+(-60*x**2+4*x)*exp(10*ln(2)-5*x-5115)**3+(-60*x**3+12*x**2)*exp(10
*ln(2)-5*x-5115)**2+(-20*x**4+12*x**3)*exp(10*ln(2)-5*x-5115)+4*x**4)*ln(x)-4*exp(10*ln(2)-5*x-5115)**4-16*x*e
xp(10*ln(2)-5*x-5115)**3-24*x**2*exp(10*ln(2)-5*x-5115)**2-16*x**3*exp(10*ln(2)-5*x-5115)-4*x**4)/x/ln(x)**5,x
)

[Out]

x**4/log(x)**4 + (4096*x**3*exp(-5*x - 5115)*log(x)**12 + 6291456*x**2*exp(-10*x - 10230)*log(x)**12 + 4294967
296*x*exp(-15*x - 15345)*log(x)**12 + 1099511627776*exp(-20*x - 20460)*log(x)**12)/log(x)**16

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