3.89.66 \(\int \frac {-9+288 x^2+(6-192 x^2) \log (x)+(-1+32 x^2) \log ^2(x)+e^{\frac {-15-3 \log (5)+5 \log (x)}{-3+\log (x)}} (-144 x^2-24 x^2 \log (5)+96 x^2 \log (x)-16 x^2 \log ^2(x))+e^{\frac {2 (-15-3 \log (5)+5 \log (x))}{-3+\log (x)}} (18 x^2+6 x^2 \log (5)-12 x^2 \log (x)+2 x^2 \log ^2(x))}{9 x-6 x \log (x)+x \log ^2(x)} \, dx\)

Optimal. Leaf size=30 \[ 7+\left (-4 x+e^{5+\frac {3 \log (5)}{3-\log (x)}} x\right )^2-\log (x) \]

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Rubi [F]  time = 6.90, 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 {-9+288 x^2+\left (6-192 x^2\right ) \log (x)+\left (-1+32 x^2\right ) \log ^2(x)+e^{\frac {-15-3 \log (5)+5 \log (x)}{-3+\log (x)}} \left (-144 x^2-24 x^2 \log (5)+96 x^2 \log (x)-16 x^2 \log ^2(x)\right )+e^{\frac {2 (-15-3 \log (5)+5 \log (x))}{-3+\log (x)}} \left (18 x^2+6 x^2 \log (5)-12 x^2 \log (x)+2 x^2 \log ^2(x)\right )}{9 x-6 x \log (x)+x \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-9 + 288*x^2 + (6 - 192*x^2)*Log[x] + (-1 + 32*x^2)*Log[x]^2 + E^((-15 - 3*Log[5] + 5*Log[x])/(-3 + Log[x
]))*(-144*x^2 - 24*x^2*Log[5] + 96*x^2*Log[x] - 16*x^2*Log[x]^2) + E^((2*(-15 - 3*Log[5] + 5*Log[x]))/(-3 + Lo
g[x]))*(18*x^2 + 6*x^2*Log[5] - 12*x^2*Log[x] + 2*x^2*Log[x]^2))/(9*x - 6*x*Log[x] + x*Log[x]^2),x]

[Out]

16*x^2 - Log[x] - 16*Defer[Int][x^((2 + Log[x])/(-3 + Log[x]))/(5^(3/(-3 + Log[x]))*E^(15/(-3 + Log[x]))), x]
+ 2*Defer[Int][x^((7 + Log[x])/(-3 + Log[x]))/(5^(6/(-3 + Log[x]))*E^(30/(-3 + Log[x]))), x] - 24*Log[5]*Defer
[Int][x^((2 + Log[x])/(-3 + Log[x]))/(5^(3/(-3 + Log[x]))*E^(15/(-3 + Log[x]))*(-3 + Log[x])^2), x] + 6*Log[5]
*Defer[Int][x^((7 + Log[x])/(-3 + Log[x]))/(5^(6/(-3 + Log[x]))*E^(30/(-3 + Log[x]))*(-3 + Log[x])^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-9+288 x^2+\left (6-192 x^2\right ) \log (x)+\left (-1+32 x^2\right ) \log ^2(x)+e^{\frac {-15-3 \log (5)+5 \log (x)}{-3+\log (x)}} \left (-144 x^2-24 x^2 \log (5)+96 x^2 \log (x)-16 x^2 \log ^2(x)\right )+e^{\frac {2 (-15-3 \log (5)+5 \log (x))}{-3+\log (x)}} \left (18 x^2+6 x^2 \log (5)-12 x^2 \log (x)+2 x^2 \log ^2(x)\right )}{x (3-\log (x))^2} \, dx\\ &=\int \left (-\frac {9}{x (-3+\log (x))^2}+\frac {288 x}{(-3+\log (x))^2}-\frac {6 \left (-1+32 x^2\right ) \log (x)}{x (-3+\log (x))^2}+\frac {\left (-1+32 x^2\right ) \log ^2(x)}{x (-3+\log (x))^2}+\frac {8\ 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \left (-18 \left (1+\frac {\log (5)}{6}\right )+12 \log (x)-2 \log ^2(x)\right )}{(3-\log (x))^2}+\frac {2\ 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \left (9 \left (1+\frac {\log (5)}{3}\right )-6 \log (x)+\log ^2(x)\right )}{(3-\log (x))^2}\right ) \, dx\\ &=2 \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \left (9 \left (1+\frac {\log (5)}{3}\right )-6 \log (x)+\log ^2(x)\right )}{(3-\log (x))^2} \, dx-6 \int \frac {\left (-1+32 x^2\right ) \log (x)}{x (-3+\log (x))^2} \, dx+8 \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \left (-18 \left (1+\frac {\log (5)}{6}\right )+12 \log (x)-2 \log ^2(x)\right )}{(3-\log (x))^2} \, dx-9 \int \frac {1}{x (-3+\log (x))^2} \, dx+288 \int \frac {x}{(-3+\log (x))^2} \, dx+\int \frac {\left (-1+32 x^2\right ) \log ^2(x)}{x (-3+\log (x))^2} \, dx\\ &=\frac {288 x^2}{3-\log (x)}+2 \int \left (5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}+\frac {3\ 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \log (5)}{(-3+\log (x))^2}\right ) \, dx-6 \int \left (\frac {3 \left (-1+32 x^2\right )}{x (-3+\log (x))^2}+\frac {-1+32 x^2}{x (-3+\log (x))}\right ) \, dx+8 \int \left (-2 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}-\frac {3\ 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \log (5)}{(-3+\log (x))^2}\right ) \, dx-9 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,-3+\log (x)\right )+576 \int \frac {x}{-3+\log (x)} \, dx+\int \left (\frac {-1+32 x^2}{x}+\frac {9 \left (-1+32 x^2\right )}{x (-3+\log (x))^2}+\frac {6 \left (-1+32 x^2\right )}{x (-3+\log (x))}\right ) \, dx\\ &=-\frac {9}{3-\log (x)}+\frac {288 x^2}{3-\log (x)}+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx+9 \int \frac {-1+32 x^2}{x (-3+\log (x))^2} \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx-18 \int \frac {-1+32 x^2}{x (-3+\log (x))^2} \, dx+576 \operatorname {Subst}\left (\int \frac {e^{2 x}}{-3+x} \, dx,x,\log (x)\right )+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx+\int \frac {-1+32 x^2}{x} \, dx\\ &=576 e^6 \text {Ei}(-2 (3-\log (x)))-\frac {9}{3-\log (x)}+\frac {288 x^2}{3-\log (x)}+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx+9 \int \left (-\frac {1}{x (-3+\log (x))^2}+\frac {32 x}{(-3+\log (x))^2}\right ) \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx-18 \int \left (-\frac {1}{x (-3+\log (x))^2}+\frac {32 x}{(-3+\log (x))^2}\right ) \, dx+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx+\int \left (-\frac {1}{x}+32 x\right ) \, dx\\ &=16 x^2+576 e^6 \text {Ei}(-2 (3-\log (x)))-\frac {9}{3-\log (x)}+\frac {288 x^2}{3-\log (x)}-\log (x)+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx-9 \int \frac {1}{x (-3+\log (x))^2} \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx+18 \int \frac {1}{x (-3+\log (x))^2} \, dx+288 \int \frac {x}{(-3+\log (x))^2} \, dx-576 \int \frac {x}{(-3+\log (x))^2} \, dx+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx\\ &=16 x^2+576 e^6 \text {Ei}(-2 (3-\log (x)))-\frac {9}{3-\log (x)}-\log (x)+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx-9 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,-3+\log (x)\right )-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx+18 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,-3+\log (x)\right )+576 \int \frac {x}{-3+\log (x)} \, dx-1152 \int \frac {x}{-3+\log (x)} \, dx+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx\\ &=16 x^2+576 e^6 \text {Ei}(-2 (3-\log (x)))-\log (x)+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx+576 \operatorname {Subst}\left (\int \frac {e^{2 x}}{-3+x} \, dx,x,\log (x)\right )-1152 \operatorname {Subst}\left (\int \frac {e^{2 x}}{-3+x} \, dx,x,\log (x)\right )+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx\\ &=16 x^2-\log (x)+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.49, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-9+288 x^2+\left (6-192 x^2\right ) \log (x)+\left (-1+32 x^2\right ) \log ^2(x)+e^{\frac {-15-3 \log (5)+5 \log (x)}{-3+\log (x)}} \left (-144 x^2-24 x^2 \log (5)+96 x^2 \log (x)-16 x^2 \log ^2(x)\right )+e^{\frac {2 (-15-3 \log (5)+5 \log (x))}{-3+\log (x)}} \left (18 x^2+6 x^2 \log (5)-12 x^2 \log (x)+2 x^2 \log ^2(x)\right )}{9 x-6 x \log (x)+x \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-9 + 288*x^2 + (6 - 192*x^2)*Log[x] + (-1 + 32*x^2)*Log[x]^2 + E^((-15 - 3*Log[5] + 5*Log[x])/(-3 +
Log[x]))*(-144*x^2 - 24*x^2*Log[5] + 96*x^2*Log[x] - 16*x^2*Log[x]^2) + E^((2*(-15 - 3*Log[5] + 5*Log[x]))/(-
3 + Log[x]))*(18*x^2 + 6*x^2*Log[5] - 12*x^2*Log[x] + 2*x^2*Log[x]^2))/(9*x - 6*x*Log[x] + x*Log[x]^2),x]

[Out]

Integrate[(-9 + 288*x^2 + (6 - 192*x^2)*Log[x] + (-1 + 32*x^2)*Log[x]^2 + E^((-15 - 3*Log[5] + 5*Log[x])/(-3 +
Log[x]))*(-144*x^2 - 24*x^2*Log[5] + 96*x^2*Log[x] - 16*x^2*Log[x]^2) + E^((2*(-15 - 3*Log[5] + 5*Log[x]))/(-
3 + Log[x]))*(18*x^2 + 6*x^2*Log[5] - 12*x^2*Log[x] + 2*x^2*Log[x]^2))/(9*x - 6*x*Log[x] + x*Log[x]^2), x]

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fricas [B]  time = 0.53, size = 57, normalized size = 1.90 \begin {gather*} -8 \, x^{2} e^{\left (-\frac {3 \, \log \relax (5) - 5 \, \log \relax (x) + 15}{\log \relax (x) - 3}\right )} + x^{2} e^{\left (-\frac {2 \, {\left (3 \, \log \relax (5) - 5 \, \log \relax (x) + 15\right )}}{\log \relax (x) - 3}\right )} + 16 \, x^{2} - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2*log(x)^2-12*x^2*log(x)+6*x^2*log(5)+18*x^2)*exp((5*log(x)-3*log(5)-15)/(log(x)-3))^2+(-16*x^
2*log(x)^2+96*x^2*log(x)-24*x^2*log(5)-144*x^2)*exp((5*log(x)-3*log(5)-15)/(log(x)-3))+(32*x^2-1)*log(x)^2+(-1
92*x^2+6)*log(x)+288*x^2-9)/(x*log(x)^2-6*x*log(x)+9*x),x, algorithm="fricas")

[Out]

-8*x^2*e^(-(3*log(5) - 5*log(x) + 15)/(log(x) - 3)) + x^2*e^(-2*(3*log(5) - 5*log(x) + 15)/(log(x) - 3)) + 16*
x^2 - log(x)

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giac [A]  time = 1.65, size = 50, normalized size = 1.67 \begin {gather*} -40 \, x^{2} e^{\left (-\frac {\log \relax (5) \log \relax (x)}{\log \relax (x) - 3} + 5\right )} + 25 \, x^{2} e^{\left (-\frac {2 \, \log \relax (5) \log \relax (x)}{\log \relax (x) - 3} + 10\right )} + 16 \, x^{2} - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2*log(x)^2-12*x^2*log(x)+6*x^2*log(5)+18*x^2)*exp((5*log(x)-3*log(5)-15)/(log(x)-3))^2+(-16*x^
2*log(x)^2+96*x^2*log(x)-24*x^2*log(5)-144*x^2)*exp((5*log(x)-3*log(5)-15)/(log(x)-3))+(32*x^2-1)*log(x)^2+(-1
92*x^2+6)*log(x)+288*x^2-9)/(x*log(x)^2-6*x*log(x)+9*x),x, algorithm="giac")

[Out]

-40*x^2*e^(-log(5)*log(x)/(log(x) - 3) + 5) + 25*x^2*e^(-2*log(5)*log(x)/(log(x) - 3) + 10) + 16*x^2 - log(x)

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maple [A]  time = 0.64, size = 58, normalized size = 1.93

method	result	size
risch	\(16 x^{2}-\ln \relax (x )+x^{2} {\mathrm e}^{-\frac {2 \left (-5 \ln \relax (x )+3 \ln \relax (5)+15\right )}{\ln \relax (x )-3}}-8 x^{2} {\mathrm e}^{-\frac {-5 \ln \relax (x )+3 \ln \relax (5)+15}{\ln \relax (x )-3}}\)	\(58\)
default	\(16 x^{2}-\ln \relax (x )+\frac {24 x^{2} {\mathrm e}^{-\frac {-5 \ln \relax (x )+3 \ln \relax (5)+15}{\ln \relax (x )-3}}-8 \ln \relax (x ) x^{2} {\mathrm e}^{-\frac {-5 \ln \relax (x )+3 \ln \relax (5)+15}{\ln \relax (x )-3}}}{\ln \relax (x )-3}+\frac {\ln \relax (x ) x^{2} {\mathrm e}^{-\frac {2 \left (-5 \ln \relax (x )+3 \ln \relax (5)+15\right )}{\ln \relax (x )-3}}-3 x^{2} {\mathrm e}^{-\frac {2 \left (-5 \ln \relax (x )+3 \ln \relax (5)+15\right )}{\ln \relax (x )-3}}}{\ln \relax (x )-3}\)	\(126\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^2*ln(x)^2-12*x^2*ln(x)+6*x^2*ln(5)+18*x^2)*exp((5*ln(x)-3*ln(5)-15)/(ln(x)-3))^2+(-16*x^2*ln(x)^2+96
*x^2*ln(x)-24*x^2*ln(5)-144*x^2)*exp((5*ln(x)-3*ln(5)-15)/(ln(x)-3))+(32*x^2-1)*ln(x)^2+(-192*x^2+6)*ln(x)+288
*x^2-9)/(x*ln(x)^2-6*x*ln(x)+9*x),x,method=_RETURNVERBOSE)

[Out]

16*x^2-ln(x)+x^2*exp(-2*(-5*ln(x)+3*ln(5)+15)/(ln(x)-3))-8*x^2*exp(-(-5*ln(x)+3*ln(5)+15)/(ln(x)-3))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {16 \, x^{2} \log \relax (x) - 48 \, x^{2} - 9}{\log \relax (x) - 3} + \frac {9}{\log \relax (x) - 3} - \int \frac {8 \, {\left (2 \, x \log \relax (x)^{2} + 3 \, x {\left (\log \relax (5) + 6\right )} - 12 \, x \log \relax (x)\right )} e^{\left (-\frac {3 \, \log \relax (5)}{\log \relax (x) - 3} + \frac {5 \, \log \relax (x)}{\log \relax (x) - 3} - \frac {15}{\log \relax (x) - 3}\right )}}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9}\,{d x} + \int \frac {2 \, {\left (x \log \relax (x)^{2} + 3 \, x {\left (\log \relax (5) + 3\right )} - 6 \, x \log \relax (x)\right )} e^{\left (-\frac {6 \, \log \relax (5)}{\log \relax (x) - 3} + \frac {10 \, \log \relax (x)}{\log \relax (x) - 3} - \frac {30}{\log \relax (x) - 3}\right )}}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9}\,{d x} - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2*log(x)^2-12*x^2*log(x)+6*x^2*log(5)+18*x^2)*exp((5*log(x)-3*log(5)-15)/(log(x)-3))^2+(-16*x^
2*log(x)^2+96*x^2*log(x)-24*x^2*log(5)-144*x^2)*exp((5*log(x)-3*log(5)-15)/(log(x)-3))+(32*x^2-1)*log(x)^2+(-1
92*x^2+6)*log(x)+288*x^2-9)/(x*log(x)^2-6*x*log(x)+9*x),x, algorithm="maxima")

[Out]

(16*x^2*log(x) - 48*x^2 - 9)/(log(x) - 3) + 9/(log(x) - 3) - integrate(8*(2*x*log(x)^2 + 3*x*(log(5) + 6) - 12
*x*log(x))*e^(-3*log(5)/(log(x) - 3) + 5*log(x)/(log(x) - 3) - 15/(log(x) - 3))/(log(x)^2 - 6*log(x) + 9), x)
+ integrate(2*(x*log(x)^2 + 3*x*(log(5) + 3) - 6*x*log(x))*e^(-6*log(5)/(log(x) - 3) + 10*log(x)/(log(x) - 3)
- 30/(log(x) - 3))/(log(x)^2 - 6*log(x) + 9), x) - log(x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{-\frac {2\,\left (3\,\ln \relax (5)-5\,\ln \relax (x)+15\right )}{\ln \relax (x)-3}}\,\left (2\,x^2\,{\ln \relax (x)}^2-12\,x^2\,\ln \relax (x)+6\,x^2\,\ln \relax (5)+18\,x^2\right )-{\mathrm {e}}^{-\frac {3\,\ln \relax (5)-5\,\ln \relax (x)+15}{\ln \relax (x)-3}}\,\left (16\,x^2\,{\ln \relax (x)}^2-96\,x^2\,\ln \relax (x)+24\,x^2\,\ln \relax (5)+144\,x^2\right )+{\ln \relax (x)}^2\,\left (32\,x^2-1\right )+288\,x^2-\ln \relax (x)\,\left (192\,x^2-6\right )-9}{x\,{\ln \relax (x)}^2-6\,x\,\ln \relax (x)+9\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(2*(3*log(5) - 5*log(x) + 15))/(log(x) - 3))*(2*x^2*log(x)^2 - 12*x^2*log(x) + 6*x^2*log(5) + 18*x^2
) - exp(-(3*log(5) - 5*log(x) + 15)/(log(x) - 3))*(16*x^2*log(x)^2 - 96*x^2*log(x) + 24*x^2*log(5) + 144*x^2)
+ log(x)^2*(32*x^2 - 1) + 288*x^2 - log(x)*(192*x^2 - 6) - 9)/(9*x + x*log(x)^2 - 6*x*log(x)),x)

[Out]

int((exp(-(2*(3*log(5) - 5*log(x) + 15))/(log(x) - 3))*(2*x^2*log(x)^2 - 12*x^2*log(x) + 6*x^2*log(5) + 18*x^2
) - exp(-(3*log(5) - 5*log(x) + 15)/(log(x) - 3))*(16*x^2*log(x)^2 - 96*x^2*log(x) + 24*x^2*log(5) + 144*x^2)
+ log(x)^2*(32*x^2 - 1) + 288*x^2 - log(x)*(192*x^2 - 6) - 9)/(9*x + x*log(x)^2 - 6*x*log(x)), x)

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sympy [B]  time = 3.14, size = 53, normalized size = 1.77 \begin {gather*} x^{2} e^{\frac {2 \left (5 \log {\relax (x )} - 15 - 3 \log {\relax (5 )}\right )}{\log {\relax (x )} - 3}} - 8 x^{2} e^{\frac {5 \log {\relax (x )} - 15 - 3 \log {\relax (5 )}}{\log {\relax (x )} - 3}} + 16 x^{2} - \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**2*ln(x)**2-12*x**2*ln(x)+6*x**2*ln(5)+18*x**2)*exp((5*ln(x)-3*ln(5)-15)/(ln(x)-3))**2+(-16*x*
*2*ln(x)**2+96*x**2*ln(x)-24*x**2*ln(5)-144*x**2)*exp((5*ln(x)-3*ln(5)-15)/(ln(x)-3))+(32*x**2-1)*ln(x)**2+(-1
92*x**2+6)*ln(x)+288*x**2-9)/(x*ln(x)**2-6*x*ln(x)+9*x),x)

[Out]

x**2*exp(2*(5*log(x) - 15 - 3*log(5))/(log(x) - 3)) - 8*x**2*exp((5*log(x) - 15 - 3*log(5))/(log(x) - 3)) + 16
*x**2 - log(x)

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