∫ 8x−6x2−2x3+(−8x−2x2) log(4+x)+eex−x2 log(−1+x+log(4+x)) (−4+3x+x2−5x3−x4+ex(−4x+3x2+x3)+(4+x+ex(4x+x2)) log(4+x)+(8x2−6x3−2x4+(−8x2−2x3) log(4+x)) log(−1+x+log(4+x)))____________________________________________________________________________________________________________________________________________ 4x2−3x3−x4+(−4x2−x3) log(4+x)+eex−x2 log(−1+x+log(4+x))(−4x+3x2+x3+(4x+x2) log(4+x)) dx

3.89.12 $\int \frac {8 x-6 x^2-2 x^3+(-8 x-2 x^2) \log (4+x)+e^{e^x-x^2 \log (-1+x+\log (4+x))} (-4+3 x+x^2-5 x^3-x^4+e^x (-4 x+3 x^2+x^3)+(4+x+e^x (4 x+x^2)) \log (4+x)+(8 x^2-6 x^3-2 x^4+(-8 x^2-2 x^3) \log (4+x)) \log (-1+x+\log (4+x)))}{4 x^2-3 x^3-x^4+(-4 x^2-x^3) \log (4+x)+e^{e^x-x^2 \log (-1+x+\log (4+x))} (-4 x+3 x^2+x^3+(4 x+x^2) \log (4+x))} \, dx$

Optimal. Leaf size=26 \[ \log \left (x \left (-e^{e^x-x^2 \log (-1+x+\log (4+x))}+x\right )\right ) \]

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Rubi [F] time = 180.00, 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[(8*x - 6*x^2 - 2*x^3 + (-8*x - 2*x^2)*Log[4 + x] + E^(E^x - x^2*Log[-1 + x + Log[4 + x]])*(-4 + 3*x + x^2

- 5*x^3 - x^4 + E^x*(-4*x + 3*x^2 + x^3) + (4 + x + E^x*(4*x + x^2))*Log[4 + x] + (8*x^2 - 6*x^3 - 2*x^4 + (-8

*x^2 - 2*x^3)*Log[4 + x])*Log[-1 + x + Log[4 + x]]))/(4*x^2 - 3*x^3 - x^4 + (-4*x^2 - x^3)*Log[4 + x] + E^(E^x

- x^2*Log[-1 + x + Log[4 + x]])*(-4*x + 3*x^2 + x^3 + (4*x + x^2)*Log[4 + x])),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A] time = 0.46, size = 37, normalized size = 1.42 \begin {gather*} \log (x)-x^2 \log (-1+x+\log (4+x))+\log \left (e^{e^x}-x (-1+x+\log (4+x))^{x^2}\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(8*x - 6*x^2 - 2*x^3 + (-8*x - 2*x^2)*Log[4 + x] + E^(E^x - x^2*Log[-1 + x + Log[4 + x]])*(-4 + 3*x

+ x^2 - 5*x^3 - x^4 + E^x*(-4*x + 3*x^2 + x^3) + (4 + x + E^x*(4*x + x^2))*Log[4 + x] + (8*x^2 - 6*x^3 - 2*x^4

+ (-8*x^2 - 2*x^3)*Log[4 + x])*Log[-1 + x + Log[4 + x]]))/(4*x^2 - 3*x^3 - x^4 + (-4*x^2 - x^3)*Log[4 + x] +

E^(E^x - x^2*Log[-1 + x + Log[4 + x]])*(-4*x + 3*x^2 + x^3 + (4*x + x^2)*Log[4 + x])),x]

[Out]

Log[x] - x^2*Log[-1 + x + Log[4 + x]] + Log[E^E^x - x*(-1 + x + Log[4 + x])^x^2]

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fricas [A] time = 0.49, size = 25, normalized size = 0.96 \begin {gather*} \log \relax (x) + \log \left (-x + e^{\left (-x^{2} \log \left (x + \log \left (x + 4\right ) - 1\right ) + e^{x}\right )}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*x^3-8*x^2)*log(4+x)-2*x^4-6*x^3+8*x^2)*log(log(4+x)+x-1)+((x^2+4*x)*exp(x)+4+x)*log(4+x)+(x^3

+3*x^2-4*x)*exp(x)-x^4-5*x^3+x^2+3*x-4)*exp(-x^2*log(log(4+x)+x-1)+exp(x))+(-2*x^2-8*x)*log(4+x)-2*x^3-6*x^2+8

*x)/(((x^2+4*x)*log(4+x)+x^3+3*x^2-4*x)*exp(-x^2*log(log(4+x)+x-1)+exp(x))+(-x^3-4*x^2)*log(4+x)-x^4-3*x^3+4*x

^2),x, algorithm="fricas")

[Out]

log(x) + log(-x + e^(-x^2*log(x + log(x + 4) - 1) + e^x))

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giac [A] time = 10.05, size = 25, normalized size = 0.96 \begin {gather*} \log \left (x - e^{\left (-x^{2} \log \left (x + \log \left (x + 4\right ) - 1\right ) + e^{x}\right )}\right ) + \log \relax (x) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*x^3-8*x^2)*log(4+x)-2*x^4-6*x^3+8*x^2)*log(log(4+x)+x-1)+((x^2+4*x)*exp(x)+4+x)*log(4+x)+(x^3

+3*x^2-4*x)*exp(x)-x^4-5*x^3+x^2+3*x-4)*exp(-x^2*log(log(4+x)+x-1)+exp(x))+(-2*x^2-8*x)*log(4+x)-2*x^3-6*x^2+8

*x)/(((x^2+4*x)*log(4+x)+x^3+3*x^2-4*x)*exp(-x^2*log(log(4+x)+x-1)+exp(x))+(-x^3-4*x^2)*log(4+x)-x^4-3*x^3+4*x

^2),x, algorithm="giac")

[Out]

log(x - e^(-x^2*log(x + log(x + 4) - 1) + e^x)) + log(x)

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maple [A] time = 0.23, size = 26, normalized size = 1.00


method	result	size

risch	$\ln \relax (x )+\ln \left (\left (\ln \left (4+x \right )+x -1\right )^{-x^{2}} {\mathrm e}^{{\mathrm e}^{x}}-x \right )$	$26$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((((-2*x^3-8*x^2)*ln(4+x)-2*x^4-6*x^3+8*x^2)*ln(ln(4+x)+x-1)+((x^2+4*x)*exp(x)+4+x)*ln(4+x)+(x^3+3*x^2-4*x

)*exp(x)-x^4-5*x^3+x^2+3*x-4)*exp(-x^2*ln(ln(4+x)+x-1)+exp(x))+(-2*x^2-8*x)*ln(4+x)-2*x^3-6*x^2+8*x)/(((x^2+4*

x)*ln(4+x)+x^3+3*x^2-4*x)*exp(-x^2*ln(ln(4+x)+x-1)+exp(x))+(-x^3-4*x^2)*ln(4+x)-x^4-3*x^3+4*x^2),x,method=_RET

URNVERBOSE)

[Out]

ln(x)+ln((ln(4+x)+x-1)^(-x^2)*exp(exp(x))-x)

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maxima [A] time = 0.46, size = 42, normalized size = 1.62 \begin {gather*} -x^{2} \log \left (x + \log \left (x + 4\right ) - 1\right ) + 2 \, \log \relax (x) + \log \left (\frac {{\left (x + \log \left (x + 4\right ) - 1\right )}^{\left (x^{2}\right )} x - e^{\left (e^{x}\right )}}{x}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*x^3-8*x^2)*log(4+x)-2*x^4-6*x^3+8*x^2)*log(log(4+x)+x-1)+((x^2+4*x)*exp(x)+4+x)*log(4+x)+(x^3

+3*x^2-4*x)*exp(x)-x^4-5*x^3+x^2+3*x-4)*exp(-x^2*log(log(4+x)+x-1)+exp(x))+(-2*x^2-8*x)*log(4+x)-2*x^3-6*x^2+8

*x)/(((x^2+4*x)*log(4+x)+x^3+3*x^2-4*x)*exp(-x^2*log(log(4+x)+x-1)+exp(x))+(-x^3-4*x^2)*log(4+x)-x^4-3*x^3+4*x

^2),x, algorithm="maxima")

[Out]

-x^2*log(x + log(x + 4) - 1) + 2*log(x) + log(((x + log(x + 4) - 1)^(x^2)*x - e^(e^x))/x)

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mupad [B] time = 6.26, size = 25, normalized size = 0.96 \begin {gather*} \ln \relax (x)+\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{{\left (x+\ln \left (x+4\right )-1\right )}^{x^2}}-x\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((log(x + 4)*(8*x + 2*x^2) - 8*x + 6*x^2 + 2*x^3 - exp(exp(x) - x^2*log(x + log(x + 4) - 1))*(3*x - log(x +

log(x + 4) - 1)*(log(x + 4)*(8*x^2 + 2*x^3) - 8*x^2 + 6*x^3 + 2*x^4) + exp(x)*(3*x^2 - 4*x + x^3) + log(x + 4

)*(x + exp(x)*(4*x + x^2) + 4) + x^2 - 5*x^3 - x^4 - 4))/(log(x + 4)*(4*x^2 + x^3) - exp(exp(x) - x^2*log(x +

log(x + 4) - 1))*(log(x + 4)*(4*x + x^2) - 4*x + 3*x^2 + x^3) - 4*x^2 + 3*x^3 + x^4),x)

[Out]

log(x) + log(exp(exp(x))/(x + log(x + 4) - 1)^(x^2) - x)

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sympy [A] time = 6.09, size = 24, normalized size = 0.92 \begin {gather*} \log {\relax (x )} + \log {\left (- x + e^{- x^{2} \log {\left (x + \log {\left (x + 4 \right )} - 1 \right )} + e^{x}} \right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*x**3-8*x**2)*ln(4+x)-2*x**4-6*x**3+8*x**2)*ln(ln(4+x)+x-1)+((x**2+4*x)*exp(x)+4+x)*ln(4+x)+(x

**3+3*x**2-4*x)*exp(x)-x**4-5*x**3+x**2+3*x-4)*exp(-x**2*ln(ln(4+x)+x-1)+exp(x))+(-2*x**2-8*x)*ln(4+x)-2*x**3-

6*x**2+8*x)/(((x**2+4*x)*ln(4+x)+x**3+3*x**2-4*x)*exp(-x**2*ln(ln(4+x)+x-1)+exp(x))+(-x**3-4*x**2)*ln(4+x)-x**

4-3*x**3+4*x**2),x)

[Out]

log(x) + log(-x + exp(-x**2*log(x + log(x + 4) - 1) + exp(x)))

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