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

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

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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 = {} $$\begin{array}{c}\int \frac{-9+288x^2+(6-192x^2)\log (x)+(-1+32x^2){\log }^2(x)+e^{\frac{-15-3\log (5)+5\log (x)}{-3+\log (x)}}(-144x^2-24x^2\log (5)+96x^2\log (x)-16x^2{\log }^2(x))+e^{\frac{2(-15-3\log (5)+5\log (x))}{-3+\log (x)}}(18x^2+6x^2\log (5)-12x^2\log (x)+2x^2{\log }^2(x))}{9x-6x\log (x)+x{\log }^2(x)}dx\end{array}$$

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{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{-9+288x^2+(6-192x^2)\log (x)+(-1+32x^2){\log }^2(x)+e^{\frac{-15-3\log (5)+5\log (x)}{-3+\log (x)}}(-144x^2-24x^2\log (5)+96x^2\log (x)-16x^2{\log }^2(x))+e^{\frac{2(-15-3\log (5)+5\log (x))}{-3+\log (x)}}(18x^2+6x^2\log (5)-12x^2\log (x)+2x^2{\log }^2(x))}{x(3-\log (x){)}^2}dx\\ & =\int (-\frac{9}{x(-3+\log (x){)}^2}+\frac{288x}{(-3+\log (x){)}^2}-\frac{6(-1+32x^2)\log (x)}{x(-3+\log (x){)}^2}+\frac{(-1+32x^2){\log }^2(x)}{x(-3+\log (x){)}^2}+\frac{85^{-\frac{3}{-3+\log (x)}}{e}^{-\frac{15}{-3+\log (x)}}{x}^{\frac{2+\log (x)}{-3+\log (x)}}(-18(1+\frac{\log (5)}{6})+12\log (x)-2{\log }^2(x))}{(3-\log (x){)}^2}+\frac{25^{-\frac{6}{-3+\log (x)}}{e}^{-\frac{30}{-3+\log (x)}}{x}^{\frac{7+\log (x)}{-3+\log (x)}}(9(1+\frac{\log (5)}{3})-6\log (x)+{\log }^2(x))}{(3-\log (x){)}^2})dx\\ & =2\int \frac{5^{-\frac{6}{-3+\log (x)}}{e}^{-\frac{30}{-3+\log (x)}}{x}^{\frac{7+\log (x)}{-3+\log (x)}}(9(1+\frac{\log (5)}{3})-6\log (x)+{\log }^2(x))}{(3-\log (x){)}^2}dx-6\int \frac{(-1+32x^2)\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)}}(-18(1+\frac{\log (5)}{6})+12\log (x)-2{\log }^2(x))}{(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{(-1+32x^2){\log }^2(x)}{x(-3+\log (x){)}^2}dx\\ & =\frac{288x^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)}}+\frac{35^{-\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})dx-6\int (\frac{3(-1+32x^2)}{x(-3+\log (x){)}^2}+\frac{-1+32x^2}{x(-3+\log (x))})dx+8\int (-25^{-\frac{3}{-3+\log (x)}}{e}^{-\frac{15}{-3+\log (x)}}{x}^{\frac{2+\log (x)}{-3+\log (x)}}-\frac{35^{-\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})dx-9\mathrm{Subst}(\int \frac{1}{x^2}dx,x,-3+\log (x))+576\int \frac{x}{-3+\log (x)}dx+\int (\frac{-1+32x^2}{x}+\frac{9(-1+32x^2)}{x(-3+\log (x){)}^2}+\frac{6(-1+32x^2)}{x(-3+\log (x))})dx\\ & =-\frac{9}{3-\log (x)}+\frac{288x^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+32x^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+32x^2}{x(-3+\log (x){)}^2}dx+576\mathrm{Subst}(\int \frac{e^{2x}}{-3+x}dx,x,\log (x))+(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+32x^2}{x}dx\\ & =576e^6\text{Ei}(-2(3-\log (x)))-\frac{9}{3-\log (x)}+\frac{288x^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}{x(-3+\log (x){)}^2}+\frac{32x}{(-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}+\frac{32x}{(-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+\int (-\frac{1}{x}+32x)dx\\ & =16x^2+576e^6\text{Ei}(-2(3-\log (x)))-\frac{9}{3-\log (x)}+\frac{288x^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\\ & =16x^2+576e^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\mathrm{Subst}(\int \frac{1}{x^2}dx,x,-3+\log (x))-16\int 5^{-\frac{3}{-3+\log (x)}}{e}^{-\frac{15}{-3+\log (x)}}{x}^{\frac{2+\log (x)}{-3+\log (x)}}dx+18\mathrm{Subst}(\int \frac{1}{x^2}dx,x,-3+\log (x))+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\\ & =16x^2+576e^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\mathrm{Subst}(\int \frac{e^{2x}}{-3+x}dx,x,\log (x))-1152\mathrm{Subst}(\int \frac{e^{2x}}{-3+x}dx,x,\log (x))+(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\\ & =16x^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{array}\end{array}$$

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

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 $$\begin{array}{c}-8x^2{e}^{(-\frac{3\log (5)-5\log (x)+15}{\log (x)-3})}+x^2{e}^{(-\frac{2(3\log (5)-5\log (x)+15)}{\log (x)-3})}+16x^2-\log (x)\end{array}$$

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 $$\begin{array}{c}-40x^2{e}^{(-\frac{\log (5)\log (x)}{\log (x)-3}+5)}+25x^2{e}^{(-\frac{2\log (5)\log (x)}{\log (x)-3}+10)}+16x^2-\log (x)\end{array}$$

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	$16x^2-\ln (x)+x^2{\mathrm{e}}^{-\frac{2(-5\ln (x)+3\ln (5)+15)}{\ln (x)-3}}-8x^2{\mathrm{e}}^{-\frac{-5\ln (x)+3\ln (5)+15}{\ln (x)-3}}$	$58$
default	$16x^2-\ln (x)+\frac{24x^2{\mathrm{e}}^{-\frac{-5\ln (x)+3\ln (5)+15}{\ln (x)-3}}-8\ln (x)x^2{\mathrm{e}}^{-\frac{-5\ln (x)+3\ln (5)+15}{\ln (x)-3}}}{\ln (x)-3}+\frac{\ln (x)x^2{\mathrm{e}}^{-\frac{2(-5\ln (x)+3\ln (5)+15)}{\ln (x)-3}}-3x^2{\mathrm{e}}^{-\frac{2(-5\ln (x)+3\ln (5)+15)}{\ln (x)-3}}}{\ln (x)-3}$	$126$

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 $$\begin{array}{c}\frac{16x^2\log (x)-48x^2-9}{\log (x)-3}+\frac{9}{\log (x)-3}-\int \frac{8(2x\log (x{)}^2+3x(\log (5)+6)-12x\log (x))e^{(-\frac{3\log (5)}{\log (x)-3}+\frac{5\log (x)}{\log (x)-3}-\frac{15}{\log (x)-3})}}{\log (x{)}^2-6\log (x)+9}dx+\int \frac{2(x\log (x{)}^2+3x(\log (5)+3)-6x\log (x))e^{(-\frac{6\log (5)}{\log (x)-3}+\frac{10\log (x)}{\log (x)-3}-\frac{30}{\log (x)-3})}}{\log (x{)}^2-6\log (x)+9}dx-\log (x)\end{array}$$

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 $$\begin{array}{c}\int \frac{{\mathrm{e}}^{-\frac{2(3\ln (5)-5\ln (x)+15)}{\ln (x)-3}}(2x^2{\ln (x)}^2-12x^2\ln (x)+6x^2\ln (5)+18x^2)-{\mathrm{e}}^{-\frac{3\ln (5)-5\ln (x)+15}{\ln (x)-3}}(16x^2{\ln (x)}^2-96x^2\ln (x)+24x^2\ln (5)+144x^2)+{\ln (x)}^2(32x^2-1)+288x^2-\ln (x)(192x^2-6)-9}{x{\ln (x)}^2-6x\ln (x)+9x}dx\end{array}$$

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 $$\begin{array}{c}{x}^2{e}^{\frac{2(5\log (x)-15-3\log (5))}{\log (x)-3}}-8x^2{e}^{\frac{5\log (x)-15-3\log (5)}{\log (x)-3}}+16x^2-\log (x)\end{array}$$

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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