3.18.11 $\int \frac{-e^{x^2}+2e^{x^2}{x}^2\log (x)+(-3x+x\log (6)){\log }^2(x)}{(-3x+x\log (6)){\log }^2(x)}dx$

Optimal. Leaf size=21 $$x-\frac{e^{x^2}}{(3-\log (6))\log (x)}$$

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Rubi [F]  time = 0.38, 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 = {} $$\begin{array}{c}\int \frac{-e^{x^2}+2e^{x^2}{x}^2\log (x)+(-3x+x\log (6)){\log }^2(x)}{(-3x+x\log (6)){\log }^2(x)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-E^x^2 + 2*E^x^2*x^2*Log[x] + (-3*x + x*Log[6])*Log[x]^2)/((-3*x + x*Log[6])*Log[x]^2),x]

[Out]

x + Defer[Int][E^x^2/(x*Log[x]^2), x]/(3 - Log[6]) - (2*Defer[Int][(E^x^2*x)/Log[x], x])/(3 - Log[6])

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{-e^{x^2}+2e^{x^2}{x}^2\log (x)+(-3x+x\log (6)){\log }^2(x)}{x(-3+\log (6)){\log }^2(x)}dx\\ & =\frac{\int \frac{-e^{x^2}+2e^{x^2}{x}^2\log (x)+(-3x+x\log (6)){\log }^2(x)}{x{\log }^2(x)}dx}{-3+\log (6)}\\ & =\frac{\int (-3+\log (6)-\frac{e^{x^2}}{x{\log }^2(x)}+\frac{2e^{x^2}x}{\log (x)})dx}{-3+\log (6)}\\ & =x-\frac{2\int \frac{e^{x^2}x}{\log (x)}dx}{3-\log (6)}-\frac{\int \frac{e^{x^2}}{x{\log }^2(x)}dx}{-3+\log (6)}\end{array}\end{array}$$

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Mathematica [A]  time = 0.11, size = 18, normalized size = 0.86 $$\begin{array}{c}x+\frac{e^{x^2}}{(-3+\log (6))\log (x)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-E^x^2 + 2*E^x^2*x^2*Log[x] + (-3*x + x*Log[6])*Log[x]^2)/((-3*x + x*Log[6])*Log[x]^2),x]

[Out]

x + E^x^2/((-3 + Log[6])*Log[x])

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fricas [A]  time = 0.71, size = 27, normalized size = 1.29 $$\begin{array}{c}\frac{(x\log (6)-3x)\log (x)+e^{\left(x^2\right)}}{(\log (6)-3)\log (x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(6)-3*x)*log(x)^2+2*x^2*exp(x^2)*log(x)-exp(x^2))/(x*log(6)-3*x)/log(x)^2,x, algorithm="frica
s")

[Out]

((x*log(6) - 3*x)*log(x) + e^(x^2))/((log(6) - 3)*log(x))

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giac [A]  time = 0.20, size = 29, normalized size = 1.38 $$\begin{array}{c}\frac{x\log (6)\log (x)-3x\log (x)+e^{\left(x^2\right)}}{\log (6)\log (x)-3\log (x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(6)-3*x)*log(x)^2+2*x^2*exp(x^2)*log(x)-exp(x^2))/(x*log(6)-3*x)/log(x)^2,x, algorithm="giac"
)

[Out]

(x*log(6)*log(x) - 3*x*log(x) + e^(x^2))/(log(6)*log(x) - 3*log(x))

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maple [A]  time = 0.12, size = 18, normalized size = 0.86

method	result	size
default	$x+\frac{{\mathrm{e}}^{x^2}}{(\ln (6)-3)\ln (x)}$	$18$
risch	$x+\frac{{\mathrm{e}}^{x^2}}{(\ln (2)+\ln (3)-3)\ln (x)}$	$20$
norman	$\frac{x\ln (x)+\frac{{\mathrm{e}}^{x^2}}{\ln (6)-3}}{\ln (x)}$	$22$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x*ln(6)-3*x)*ln(x)^2+2*x^2*exp(x^2)*ln(x)-exp(x^2))/(x*ln(6)-3*x)/ln(x)^2,x,method=_RETURNVERBOSE)

[Out]

x+1/(ln(6)-3)*exp(x^2)/ln(x)

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maxima [A]  time = 0.64, size = 28, normalized size = 1.33 $$\begin{array}{c}\frac{x(\log (3)+\log (2)-3)\log (x)+e^{\left(x^2\right)}}{(\log (3)+\log (2)-3)\log (x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(6)-3*x)*log(x)^2+2*x^2*exp(x^2)*log(x)-exp(x^2))/(x*log(6)-3*x)/log(x)^2,x, algorithm="maxim
a")

[Out]

(x*(log(3) + log(2) - 3)*log(x) + e^(x^2))/((log(3) + log(2) - 3)*log(x))

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mupad [B]  time = 1.32, size = 17, normalized size = 0.81 $$\begin{array}{c}x+\frac{{\mathrm{e}}^{x^2}}{\ln (x)(\ln (6)-3)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x^2) + log(x)^2*(3*x - x*log(6)) - 2*x^2*exp(x^2)*log(x))/(log(x)^2*(3*x - x*log(6))),x)

[Out]

x + exp(x^2)/(log(x)*(log(6) - 3))

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sympy [A]  time = 0.27, size = 17, normalized size = 0.81 $$\begin{array}{c}x+\frac{e^{x^2}}{-3\log (x)+\log (6)\log (x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*ln(6)-3*x)*ln(x)**2+2*x**2*exp(x**2)*ln(x)-exp(x**2))/(x*ln(6)-3*x)/ln(x)**2,x)

[Out]

x + exp(x**2)/(-3*log(x) + log(6)*log(x))

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