3.1.95 $\int \frac{e^{\frac{-x+(5+x^3)\log (e^{e^{6x}}x)}{\log (e^{e^{6x}}x)}}(1+6e^{6x}x-\log (e^{e^{6x}}x)+3x^2{\log }^2(e^{e^{6x}}x))}{{\log }^2(e^{e^{6x}}x)}dx$

Optimal. Leaf size=22 $$e^{5+x^3-\frac{x}{\log \left(e^{e^{6x}}x\right)}}$$

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Rubi [A]  time = 1.36, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 87, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.023, Rules used = {6688, 6706} $$\begin{array}{c}{e}^{x^3-\frac{x}{\log \left(e^{e^{6x}}x\right)}+5}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(E^((-x + (5 + x^3)*Log[E^E^(6*x)*x])/Log[E^E^(6*x)*x])*(1 + 6*E^(6*x)*x - Log[E^E^(6*x)*x] + 3*x^2*Log[E^
E^(6*x)*x]^2))/Log[E^E^(6*x)*x]^2,x]

[Out]

E^(5 + x^3 - x/Log[E^E^(6*x)*x])

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^{5+x^3-\frac{x}{\log \left(e^{e^{6x}}x\right)}}(1+6e^{6x}x-\log \left(e^{e^{6x}}x\right)+3x^2{\log }^2\left(e^{e^{6x}}x\right))}{{\log }^2\left(e^{e^{6x}}x\right)}dx\\ & =e^{5+x^3-\frac{x}{\log \left(e^{e^{6x}}x\right)}}\end{array}\end{array}$$

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Mathematica [A]  time = 1.01, size = 22, normalized size = 1.00 $$\begin{array}{c}{e}^{5+x^3-\frac{x}{\log \left(e^{e^{6x}}x\right)}}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^((-x + (5 + x^3)*Log[E^E^(6*x)*x])/Log[E^E^(6*x)*x])*(1 + 6*E^(6*x)*x - Log[E^E^(6*x)*x] + 3*x^2*
Log[E^E^(6*x)*x]^2))/Log[E^E^(6*x)*x]^2,x]

[Out]

E^(5 + x^3 - x/Log[E^E^(6*x)*x])

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fricas [A]  time = 0.65, size = 30, normalized size = 1.36 $$\begin{array}{c}{e}^{\left(\frac{(x^3+5)\log \left(x{e}^{\left(e^{\left(6x\right)}\right)}\right)-x}{\log \left(x{e}^{\left(e^{\left(6x\right)}\right)}\right)}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x^2*log(x*exp(exp(3*x)^2))^2-log(x*exp(exp(3*x)^2))+6*x*exp(3*x)^2+1)*exp(((x^3+5)*log(x*exp(exp(
3*x)^2))-x)/log(x*exp(exp(3*x)^2)))/log(x*exp(exp(3*x)^2))^2,x, algorithm="fricas")

[Out]

e^(((x^3 + 5)*log(x*e^(e^(6*x))) - x)/log(x*e^(e^(6*x))))

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giac [A]  time = 0.55, size = 19, normalized size = 0.86 $$\begin{array}{c}{e}^{(x^3-\frac{x}{\log \left(x{e}^{\left(e^{\left(6x\right)}\right)}\right)}+5)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x^2*log(x*exp(exp(3*x)^2))^2-log(x*exp(exp(3*x)^2))+6*x*exp(3*x)^2+1)*exp(((x^3+5)*log(x*exp(exp(
3*x)^2))-x)/log(x*exp(exp(3*x)^2)))/log(x*exp(exp(3*x)^2))^2,x, algorithm="giac")

[Out]

e^(x^3 - x/log(x*e^(e^(6*x))) + 5)

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maple [C]  time = 1.57, size = 334, normalized size = 15.18

method	result	size
risch	${\mathrm{e}}^{\frac{-i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^3{x}^3+i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^2\mathrm{csgn}\left(ix\right)x^3+i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^2\mathrm{csgn}\left(i{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)x^3-i\pi \mathrm{csgn}\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)\mathrm{csgn}\left(ix\right)\mathrm{csgn}\left(i{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)x^3-5i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^3+5i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^2\mathrm{csgn}\left(ix\right)+5i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^2\mathrm{csgn}\left(i{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)-5i\pi \mathrm{csgn}\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)\mathrm{csgn}\left(ix\right)\mathrm{csgn}\left(i{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)+2x^3\ln (x)+2\ln \left({\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)x^3+10\ln (x)+10\ln \left({\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)-2x}{-i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^3+i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^2\mathrm{csgn}\left(ix\right)+i\pi \mathrm{csgn}{\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}^2\mathrm{csgn}\left(i{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)-i\pi \mathrm{csgn}\left(ix{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)\mathrm{csgn}\left(ix\right)\mathrm{csgn}\left(i{\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)+2\ln (x)+2\ln \left({\mathrm{e}}^{{\mathrm{e}}^{6x}}\right)}}$	$334$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x^2*ln(x*exp(exp(3*x)^2))^2-ln(x*exp(exp(3*x)^2))+6*x*exp(3*x)^2+1)*exp(((x^3+5)*ln(x*exp(exp(3*x)^2))-
x)/ln(x*exp(exp(3*x)^2)))/ln(x*exp(exp(3*x)^2))^2,x,method=_RETURNVERBOSE)

[Out]

exp((-I*Pi*csgn(I*x*exp(exp(6*x)))^3*x^3+I*Pi*csgn(I*x*exp(exp(6*x)))^2*csgn(I*x)*x^3+I*Pi*csgn(I*x*exp(exp(6*
x)))^2*csgn(I*exp(exp(6*x)))*x^3-I*Pi*csgn(I*x*exp(exp(6*x)))*csgn(I*x)*csgn(I*exp(exp(6*x)))*x^3-5*I*Pi*csgn(
I*x*exp(exp(6*x)))^3+5*I*Pi*csgn(I*x*exp(exp(6*x)))^2*csgn(I*x)+5*I*Pi*csgn(I*x*exp(exp(6*x)))^2*csgn(I*exp(ex
p(6*x)))-5*I*Pi*csgn(I*x*exp(exp(6*x)))*csgn(I*x)*csgn(I*exp(exp(6*x)))+2*x^3*ln(x)+2*ln(exp(exp(6*x)))*x^3+10
*ln(x)+10*ln(exp(exp(6*x)))-2*x)/(-I*Pi*csgn(I*x*exp(exp(6*x)))^3+I*Pi*csgn(I*x*exp(exp(6*x)))^2*csgn(I*x)+I*P
i*csgn(I*x*exp(exp(6*x)))^2*csgn(I*exp(exp(6*x)))-I*Pi*csgn(I*x*exp(exp(6*x)))*csgn(I*x)*csgn(I*exp(exp(6*x)))
+2*ln(x)+2*ln(exp(exp(6*x)))))

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maxima [A]  time = 0.85, size = 18, normalized size = 0.82 $$\begin{array}{c}{e}^{(x^3-\frac{x}{e^{\left(6x\right)}+\log (x)}+5)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x^2*log(x*exp(exp(3*x)^2))^2-log(x*exp(exp(3*x)^2))+6*x*exp(3*x)^2+1)*exp(((x^3+5)*log(x*exp(exp(
3*x)^2))-x)/log(x*exp(exp(3*x)^2)))/log(x*exp(exp(3*x)^2))^2,x, algorithm="maxima")

[Out]

e^(x^3 - x/(e^(6*x) + log(x)) + 5)

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mupad [B]  time = 0.38, size = 65, normalized size = 2.95 $$\begin{array}{c}{x}^{\frac{x^3+5}{{\mathrm{e}}^{6x}+\ln (x)}}{\mathrm{e}}^{-\frac{x}{{\mathrm{e}}^{6x}+\ln (x)}}{\mathrm{e}}^{\frac{x^3{\mathrm{e}}^{6x}}{{\mathrm{e}}^{6x}+\ln (x)}}{\mathrm{e}}^{\frac{5{\mathrm{e}}^{6x}}{{\mathrm{e}}^{6x}+\ln (x)}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(x - log(x*exp(exp(6*x)))*(x^3 + 5))/log(x*exp(exp(6*x))))*(6*x*exp(6*x) - log(x*exp(exp(6*x))) + 3*
x^2*log(x*exp(exp(6*x)))^2 + 1))/log(x*exp(exp(6*x)))^2,x)

[Out]

x^((x^3 + 5)/(exp(6*x) + log(x)))*exp(-x/(exp(6*x) + log(x)))*exp((x^3*exp(6*x))/(exp(6*x) + log(x)))*exp((5*e
xp(6*x))/(exp(6*x) + log(x)))

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Timed out}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x**2*ln(x*exp(exp(3*x)**2))**2-ln(x*exp(exp(3*x)**2))+6*x*exp(3*x)**2+1)*exp(((x**3+5)*ln(x*exp(e
xp(3*x)**2))-x)/ln(x*exp(exp(3*x)**2)))/ln(x*exp(exp(3*x)**2))**2,x)

[Out]

Timed out

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