3.50.6 \(\int \frac {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} (-12+57 x+12 x^2)}{4+x}+(24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}) \log (x+\frac {e^{-1+x}}{4+x})}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} (-4 x+15 x^2+4 x^3)}{4+x}+(-16 x^2-4 x^3+\frac {e^{-1+x} (-16 x-4 x^2)}{4+x}) \log (x+\frac {e^{-1+x}}{4+x})+(e^{-1+x}+4 x+x^2) \log ^2(x+\frac {e^{-1+x}}{4+x})} \, dx\)

Optimal. Leaf size=32 \[ 3 \log \left (x-x^2 \left (-2+\frac {\log \left (x+\frac {e^{-1+x}}{4+x}\right )}{x}\right )^2\right ) \]

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Rubi [F]  time = 8.07, 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 {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} \left (-12+57 x+12 x^2\right )}{4+x}+\left (24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} \left (-4 x+15 x^2+4 x^3\right )}{4+x}+\left (-16 x^2-4 x^3+\frac {e^{-1+x} \left (-16 x-4 x^2\right )}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\left (e^{-1+x}+4 x+x^2\right ) \log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-60*x + 81*x^2 + 24*x^3 + (E^(-1 + x)*(-12 + 57*x + 12*x^2))/(4 + x) + (24 - 42*x - 12*x^2 + (E^(-1 + x)*
(-30 - 6*x))/(4 + x))*Log[x + E^(-1 + x)/(4 + x)])/(-4*x^2 + 15*x^3 + 4*x^4 + (E^(-1 + x)*(-4*x + 15*x^2 + 4*x
^3))/(4 + x) + (-16*x^2 - 4*x^3 + (E^(-1 + x)*(-16*x - 4*x^2))/(4 + x))*Log[x + E^(-1 + x)/(4 + x)] + (E^(-1 +
x) + 4*x + x^2)*Log[x + E^(-1 + x)/(4 + x)]^2),x]

[Out]

9*Defer[Int][(-x + 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 + x)]^2)^(-1), x] + 12*Defe
r[Int][x/(-x + 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 + x)]^2), x] - 48*Defer[Int][1/
((4 + x)*(-x + 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 + x)]^2)), x] - 48*E*Defer[Int]
[x/((E^x + 4*E*x + E*x^2)*(-x + 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 + x)]^2)), x]
+ 24*E*Defer[Int][x^2/((E^x + 4*E*x + E*x^2)*(-x + 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x
)/(4 + x)]^2)), x] + 12*E*Defer[Int][x^3/((E^x + 4*E*x + E*x^2)*(-x + 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)]
+ Log[x + E^(-1 + x)/(4 + x)]^2)), x] - 6*Defer[Int][Log[x + E^(-1 + x)/(4 + x)]/(-x + 4*x^2 - 4*x*Log[x + E^(
-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 + x)]^2), x] - 6*Defer[Int][Log[x + E^(-1 + x)/(4 + x)]/((4 + x)*(-x
+ 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 + x)]^2)), x] + 24*E*Defer[Int][Log[x + E^(-
1 + x)/(4 + x)]/((E^x + 4*E*x + E*x^2)*(-x + 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 +
x)]^2)), x] - 12*E*Defer[Int][(x*Log[x + E^(-1 + x)/(4 + x)])/((E^x + 4*E*x + E*x^2)*(-x + 4*x^2 - 4*x*Log[x
+ E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 + x)]^2)), x] - 6*E*Defer[Int][(x^2*Log[x + E^(-1 + x)/(4 + x)])
/((E^x + 4*E*x + E*x^2)*(-x + 4*x^2 - 4*x*Log[x + E^(-1 + x)/(4 + x)] + Log[x + E^(-1 + x)/(4 + x)]^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (e x (4+x)^2 (-5+8 x)+e^x \left (-4+19 x+4 x^2\right )-2 \left (e^x (5+x)+e (4+x)^2 (-1+2 x)\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )\right )}{(4+x) \left (e^x+e x (4+x)\right ) \left (x (-1+4 x)-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx\\ &=3 \int \frac {e x (4+x)^2 (-5+8 x)+e^x \left (-4+19 x+4 x^2\right )-2 \left (e^x (5+x)+e (4+x)^2 (-1+2 x)\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{(4+x) \left (e^x+e x (4+x)\right ) \left (x (-1+4 x)-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx\\ &=3 \int \left (\frac {2 e \left (-4+2 x+x^2\right ) \left (2 x-\log \left (x+\frac {e^{-1+x}}{4+x}\right )\right )}{\left (e^x+4 e x+e x^2\right ) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}+\frac {-4+19 x+4 x^2-10 \log \left (x+\frac {e^{-1+x}}{4+x}\right )-2 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}\right ) \, dx\\ &=3 \int \frac {-4+19 x+4 x^2-10 \log \left (x+\frac {e^{-1+x}}{4+x}\right )-2 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx+(6 e) \int \frac {\left (-4+2 x+x^2\right ) \left (2 x-\log \left (x+\frac {e^{-1+x}}{4+x}\right )\right )}{\left (e^x+4 e x+e x^2\right ) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx\\ &=3 \int \left (-\frac {4}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}+\frac {19 x}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}+\frac {4 x^2}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}-\frac {10 \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}-\frac {2 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}\right ) \, dx+(6 e) \int \left (-\frac {4 \left (2 x-\log \left (x+\frac {e^{-1+x}}{4+x}\right )\right )}{\left (e^x+4 e x+e x^2\right ) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}+\frac {2 x \left (2 x-\log \left (x+\frac {e^{-1+x}}{4+x}\right )\right )}{\left (e^x+4 e x+e x^2\right ) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}+\frac {x^2 \left (2 x-\log \left (x+\frac {e^{-1+x}}{4+x}\right )\right )}{\left (e^x+4 e x+e x^2\right ) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )}\right ) \, dx\\ &=-\left (6 \int \frac {x \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx\right )-12 \int \frac {1}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx+12 \int \frac {x^2}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx-30 \int \frac {\log \left (x+\frac {e^{-1+x}}{4+x}\right )}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx+57 \int \frac {x}{(4+x) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx+(6 e) \int \frac {x^2 \left (2 x-\log \left (x+\frac {e^{-1+x}}{4+x}\right )\right )}{\left (e^x+4 e x+e x^2\right ) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx+(12 e) \int \frac {x \left (2 x-\log \left (x+\frac {e^{-1+x}}{4+x}\right )\right )}{\left (e^x+4 e x+e x^2\right ) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx-(24 e) \int \frac {2 x-\log \left (x+\frac {e^{-1+x}}{4+x}\right )}{\left (e^x+4 e x+e x^2\right ) \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.24, size = 45, normalized size = 1.41 \begin {gather*} 3 \log \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-60*x + 81*x^2 + 24*x^3 + (E^(-1 + x)*(-12 + 57*x + 12*x^2))/(4 + x) + (24 - 42*x - 12*x^2 + (E^(-1
+ x)*(-30 - 6*x))/(4 + x))*Log[x + E^(-1 + x)/(4 + x)])/(-4*x^2 + 15*x^3 + 4*x^4 + (E^(-1 + x)*(-4*x + 15*x^2
+ 4*x^3))/(4 + x) + (-16*x^2 - 4*x^3 + (E^(-1 + x)*(-16*x - 4*x^2))/(4 + x))*Log[x + E^(-1 + x)/(4 + x)] + (E
^(-1 + x) + 4*x + x^2)*Log[x + E^(-1 + x)/(4 + x)]^2),x]

[Out]

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

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fricas [A]  time = 1.12, size = 43, normalized size = 1.34 \begin {gather*} 3 \, \log \left (4 \, x^{2} - 4 \, x \log \left (x + e^{\left (x - \log \left (x + 4\right ) - 1\right )}\right ) + \log \left (x + e^{\left (x - \log \left (x + 4\right ) - 1\right )}\right )^{2} - x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x-30)*exp(-log(4+x)+x-1)-12*x^2-42*x+24)*log(exp(-log(4+x)+x-1)+x)+(12*x^2+57*x-12)*exp(-log(4
+x)+x-1)+24*x^3+81*x^2-60*x)/(((4+x)*exp(-log(4+x)+x-1)+x^2+4*x)*log(exp(-log(4+x)+x-1)+x)^2+((-4*x^2-16*x)*ex
p(-log(4+x)+x-1)-4*x^3-16*x^2)*log(exp(-log(4+x)+x-1)+x)+(4*x^3+15*x^2-4*x)*exp(-log(4+x)+x-1)+4*x^4+15*x^3-4*
x^2),x, algorithm="fricas")

[Out]

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

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giac [B]  time = 1.20, size = 105, normalized size = 3.28 \begin {gather*} 3 \, \log \left (4 \, x^{2} - 4 \, x \log \left (x^{2} e + 4 \, x e + e^{x}\right ) + \log \left (x^{2} e + 4 \, x e + e^{x}\right )^{2} + 4 \, x \log \left (x + 4\right ) - 2 \, \log \left (x^{2} e + 4 \, x e + e^{x}\right ) \log \left (x + 4\right ) + \log \left (x + 4\right )^{2} + 3 \, x - 2 \, \log \left (x^{2} e + 4 \, x e + e^{x}\right ) + 2 \, \log \left (x + 4\right ) + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x-30)*exp(-log(4+x)+x-1)-12*x^2-42*x+24)*log(exp(-log(4+x)+x-1)+x)+(12*x^2+57*x-12)*exp(-log(4
+x)+x-1)+24*x^3+81*x^2-60*x)/(((4+x)*exp(-log(4+x)+x-1)+x^2+4*x)*log(exp(-log(4+x)+x-1)+x)^2+((-4*x^2-16*x)*ex
p(-log(4+x)+x-1)-4*x^3-16*x^2)*log(exp(-log(4+x)+x-1)+x)+(4*x^3+15*x^2-4*x)*exp(-log(4+x)+x-1)+4*x^4+15*x^3-4*
x^2),x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.07, size = 43, normalized size = 1.34

method	result	size
risch	\(3 \ln \left (\ln \left (\frac {{\mathrm e}^{x -1}}{4+x}+x \right )^{2}-4 \ln \left (\frac {{\mathrm e}^{x -1}}{4+x}+x \right ) x +x \left (4 x -1\right )\right )\)	\(43\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-6*x-30)*exp(-ln(4+x)+x-1)-12*x^2-42*x+24)*ln(exp(-ln(4+x)+x-1)+x)+(12*x^2+57*x-12)*exp(-ln(4+x)+x-1)+2
4*x^3+81*x^2-60*x)/(((4+x)*exp(-ln(4+x)+x-1)+x^2+4*x)*ln(exp(-ln(4+x)+x-1)+x)^2+((-4*x^2-16*x)*exp(-ln(4+x)+x-
1)-4*x^3-16*x^2)*ln(exp(-ln(4+x)+x-1)+x)+(4*x^3+15*x^2-4*x)*exp(-ln(4+x)+x-1)+4*x^4+15*x^3-4*x^2),x,method=_RE
TURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.52, size = 73, normalized size = 2.28 \begin {gather*} 3 \, \log \left (4 \, x^{2} - 2 \, {\left (2 \, x + \log \left (x + 4\right ) + 1\right )} \log \left (x^{2} e + 4 \, x e + e^{x}\right ) + \log \left (x^{2} e + 4 \, x e + e^{x}\right )^{2} + 2 \, {\left (2 \, x + 1\right )} \log \left (x + 4\right ) + \log \left (x + 4\right )^{2} + 3 \, x + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x-30)*exp(-log(4+x)+x-1)-12*x^2-42*x+24)*log(exp(-log(4+x)+x-1)+x)+(12*x^2+57*x-12)*exp(-log(4
+x)+x-1)+24*x^3+81*x^2-60*x)/(((4+x)*exp(-log(4+x)+x-1)+x^2+4*x)*log(exp(-log(4+x)+x-1)+x)^2+((-4*x^2-16*x)*ex
p(-log(4+x)+x-1)-4*x^3-16*x^2)*log(exp(-log(4+x)+x-1)+x)+(4*x^3+15*x^2-4*x)*exp(-log(4+x)+x-1)+4*x^4+15*x^3-4*
x^2),x, algorithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (12\,x^2+57\,x-12\right )-\ln \left (x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\right )\,\left (42\,x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (6\,x+30\right )+12\,x^2-24\right )-60\,x+81\,x^2+24\,x^3}{{\ln \left (x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\right )}^2\,\left (4\,x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (x+4\right )+x^2\right )-4\,x^2+15\,x^3+4\,x^4+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (4\,x^3+15\,x^2-4\,x\right )-\ln \left (x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\right )\,\left ({\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (4\,x^2+16\,x\right )+16\,x^2+4\,x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x - log(x + 4) - 1)*(57*x + 12*x^2 - 12) - log(x + exp(x - log(x + 4) - 1))*(42*x + exp(x - log(x + 4
) - 1)*(6*x + 30) + 12*x^2 - 24) - 60*x + 81*x^2 + 24*x^3)/(log(x + exp(x - log(x + 4) - 1))^2*(4*x + exp(x -
log(x + 4) - 1)*(x + 4) + x^2) - 4*x^2 + 15*x^3 + 4*x^4 + exp(x - log(x + 4) - 1)*(15*x^2 - 4*x + 4*x^3) - log
(x + exp(x - log(x + 4) - 1))*(exp(x - log(x + 4) - 1)*(16*x + 4*x^2) + 16*x^2 + 4*x^3)),x)

[Out]

int((exp(x - log(x + 4) - 1)*(57*x + 12*x^2 - 12) - log(x + exp(x - log(x + 4) - 1))*(42*x + exp(x - log(x + 4
) - 1)*(6*x + 30) + 12*x^2 - 24) - 60*x + 81*x^2 + 24*x^3)/(log(x + exp(x - log(x + 4) - 1))^2*(4*x + exp(x -
log(x + 4) - 1)*(x + 4) + x^2) - 4*x^2 + 15*x^3 + 4*x^4 + exp(x - log(x + 4) - 1)*(15*x^2 - 4*x + 4*x^3) - log
(x + exp(x - log(x + 4) - 1))*(exp(x - log(x + 4) - 1)*(16*x + 4*x^2) + 16*x^2 + 4*x^3)), x)

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sympy [A]  time = 1.79, size = 37, normalized size = 1.16 \begin {gather*} 3 \log {\left (4 x^{2} - 4 x \log {\left (x + \frac {e^{x - 1}}{x + 4} \right )} - x + \log {\left (x + \frac {e^{x - 1}}{x + 4} \right )}^{2} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x-30)*exp(-ln(4+x)+x-1)-12*x**2-42*x+24)*ln(exp(-ln(4+x)+x-1)+x)+(12*x**2+57*x-12)*exp(-ln(4+x
)+x-1)+24*x**3+81*x**2-60*x)/(((4+x)*exp(-ln(4+x)+x-1)+x**2+4*x)*ln(exp(-ln(4+x)+x-1)+x)**2+((-4*x**2-16*x)*ex
p(-ln(4+x)+x-1)-4*x**3-16*x**2)*ln(exp(-ln(4+x)+x-1)+x)+(4*x**3+15*x**2-4*x)*exp(-ln(4+x)+x-1)+4*x**4+15*x**3-
4*x**2),x)

[Out]

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

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