3.76.25 \(\int \frac {-24 x^3+6 x^4+e^x (-4 x^3+x^4)+e^{4 x+2 x^2} (4 x^3+15 x^4+12 x^5-4 x^6)+(-4+x)^{2/x} (-24 x+6 x^2+e^{4 x+2 x^2} (4 x+15 x^2+12 x^3-4 x^4))+(-4+x)^{\frac {1}{x}} (-48 x^2+12 x^3+e^x (-5 x-3 x^2+x^3)+e^{4 x+2 x^2} (8 x^2+30 x^3+24 x^4-8 x^5)+e^x (-4+x) \log (-4+x))}{-4 x^3+x^4+(-4+x)^{2/x} (-4 x+x^2)+(-4+x)^{\frac {1}{x}} (-8 x^2+2 x^3)} \, dx\)

Optimal. Leaf size=29 \[ x \left (6-e^{2 x (2+x)}+\frac {e^x}{(-4+x)^{\frac {1}{x}}+x}\right ) \]

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Rubi [F]  time = 10.75, 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 {-24 x^3+6 x^4+e^x \left (-4 x^3+x^4\right )+e^{4 x+2 x^2} \left (4 x^3+15 x^4+12 x^5-4 x^6\right )+(-4+x)^{2/x} \left (-24 x+6 x^2+e^{4 x+2 x^2} \left (4 x+15 x^2+12 x^3-4 x^4\right )\right )+(-4+x)^{\frac {1}{x}} \left (-48 x^2+12 x^3+e^x \left (-5 x-3 x^2+x^3\right )+e^{4 x+2 x^2} \left (8 x^2+30 x^3+24 x^4-8 x^5\right )+e^x (-4+x) \log (-4+x)\right )}{-4 x^3+x^4+(-4+x)^{2/x} \left (-4 x+x^2\right )+(-4+x)^{\frac {1}{x}} \left (-8 x^2+2 x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-24*x^3 + 6*x^4 + E^x*(-4*x^3 + x^4) + E^(4*x + 2*x^2)*(4*x^3 + 15*x^4 + 12*x^5 - 4*x^6) + (-4 + x)^(2/x)
*(-24*x + 6*x^2 + E^(4*x + 2*x^2)*(4*x + 15*x^2 + 12*x^3 - 4*x^4)) + (-4 + x)^x^(-1)*(-48*x^2 + 12*x^3 + E^x*(
-5*x - 3*x^2 + x^3) + E^(4*x + 2*x^2)*(8*x^2 + 30*x^3 + 24*x^4 - 8*x^5) + E^x*(-4 + x)*Log[-4 + x]))/(-4*x^3 +
x^4 + (-4 + x)^(2/x)*(-4*x + x^2) + (-4 + x)^x^(-1)*(-8*x^2 + 2*x^3)),x]

[Out]

6*x - E^(4*x + 2*x^2)*x + Defer[Int][E^x/((-4 + x)^x^(-1) + x)^2, x] - Log[-4 + x]*Defer[Int][E^x/((-4 + x)^x^
(-1) + x)^2, x] + 4*Defer[Int][E^x/((-4 + x)*((-4 + x)^x^(-1) + x)^2), x] - Defer[Int][(E^x*x)/((-4 + x)^x^(-1
) + x)^2, x] + Defer[Int][E^x/((-4 + x)^x^(-1) + x), x] - Defer[Int][E^x/((-4 + x)*((-4 + x)^x^(-1) + x)), x]
+ Log[-4 + x]*Defer[Int][E^x/(x*((-4 + x)^x^(-1) + x)), x] + Defer[Int][(E^x*x)/((-4 + x)^x^(-1) + x), x] + De
fer[Int][Defer[Int][E^x/((-4 + x)^x^(-1) + x)^2, x]/(-4 + x), x] - Defer[Int][Defer[Int][E^x/(x*((-4 + x)^x^(-
1) + x)), x]/(-4 + x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-x \left (6 (-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2-e^{2 x (2+x)} (-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2 (1+2 x)^2+e^x \left (-5 (-4+x)^{\frac {1}{x}}-3 (-4+x)^{\frac {1}{x}} x+\left (-4+(-4+x)^{\frac {1}{x}}\right ) x^2+x^3\right )\right )-e^x (-4+x)^{1+\frac {1}{x}} \log (-4+x)}{(4-x) x \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx\\ &=\int \left (6-e^{2 x (2+x)}-4 e^{2 x (2+x)} x-4 e^{2 x (2+x)} x^2-\frac {e^x \left (-5 x+x^2-4 \log (-4+x)+x \log (-4+x)\right )}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2}+\frac {e^x \left (-5 x-3 x^2+x^3-4 \log (-4+x)+x \log (-4+x)\right )}{(-4+x) x \left ((-4+x)^{\frac {1}{x}}+x\right )}\right ) \, dx\\ &=6 x-4 \int e^{2 x (2+x)} x \, dx-4 \int e^{2 x (2+x)} x^2 \, dx-\int e^{2 x (2+x)} \, dx-\int \frac {e^x \left (-5 x+x^2-4 \log (-4+x)+x \log (-4+x)\right )}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+\int \frac {e^x \left (-5 x-3 x^2+x^3-4 \log (-4+x)+x \log (-4+x)\right )}{(-4+x) x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx\\ &=6 x-4 \int e^{4 x+2 x^2} x \, dx-4 \int e^{4 x+2 x^2} x^2 \, dx-\int e^{4 x+2 x^2} \, dx-\int \left (-\frac {5 e^x x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2}+\frac {e^x x^2}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2}-\frac {4 e^x \log (-4+x)}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2}+\frac {e^x x \log (-4+x)}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2}\right ) \, dx+\int \left (\frac {e^x \left (-5 x-3 x^2+x^3-4 \log (-4+x)+x \log (-4+x)\right )}{4 (-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}-\frac {e^x \left (-5 x-3 x^2+x^3-4 \log (-4+x)+x \log (-4+x)\right )}{4 x \left ((-4+x)^{\frac {1}{x}}+x\right )}\right ) \, dx\\ &=-e^{4 x+2 x^2}+6 x-e^{4 x+2 x^2} x+\frac {1}{4} \int \frac {e^x \left (-5 x-3 x^2+x^3-4 \log (-4+x)+x \log (-4+x)\right )}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-\frac {1}{4} \int \frac {e^x \left (-5 x-3 x^2+x^3-4 \log (-4+x)+x \log (-4+x)\right )}{x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx+4 \int e^{4 x+2 x^2} \, dx+4 \int e^{4 x+2 x^2} x \, dx+4 \int \frac {e^x \log (-4+x)}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+5 \int \frac {e^x x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\frac {\int e^{\frac {1}{8} (4+4 x)^2} \, dx}{e^2}+\int e^{4 x+2 x^2} \, dx-\int \frac {e^x x^2}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\int \frac {e^x x \log (-4+x)}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx\\ &=6 x-e^{4 x+2 x^2} x-\frac {\sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (1+x)\right )}{2 e^2}-\frac {1}{4} \int \left (-\frac {5 e^x}{(-4+x)^{\frac {1}{x}}+x}-\frac {3 e^x x}{(-4+x)^{\frac {1}{x}}+x}+\frac {e^x x^2}{(-4+x)^{\frac {1}{x}}+x}+\frac {e^x \log (-4+x)}{(-4+x)^{\frac {1}{x}}+x}-\frac {4 e^x \log (-4+x)}{x \left ((-4+x)^{\frac {1}{x}}+x\right )}\right ) \, dx+\frac {1}{4} \int \left (-\frac {5 e^x x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}-\frac {3 e^x x^2}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}+\frac {e^x x^3}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}-\frac {4 e^x \log (-4+x)}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}+\frac {e^x x \log (-4+x)}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}\right ) \, dx-4 \int e^{4 x+2 x^2} \, dx-4 \int \frac {\int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx}{-4+x} \, dx+5 \int \left (\frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2}+\frac {4 e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2}\right ) \, dx+\frac {\int e^{\frac {1}{8} (4+4 x)^2} \, dx}{e^2}+\frac {4 \int e^{\frac {1}{8} (4+4 x)^2} \, dx}{e^2}-\log (-4+x) \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\int \left (\frac {4 e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2}+\frac {16 e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2}+\frac {e^x x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2}\right ) \, dx+\int \frac {\int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+4 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx}{-4+x} \, dx\\ &=6 x-e^{4 x+2 x^2} x+\frac {\sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (1+x)\right )}{e^2}-\frac {1}{4} \int \frac {e^x x^2}{(-4+x)^{\frac {1}{x}}+x} \, dx+\frac {1}{4} \int \frac {e^x x^3}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-\frac {1}{4} \int \frac {e^x \log (-4+x)}{(-4+x)^{\frac {1}{x}}+x} \, dx+\frac {1}{4} \int \frac {e^x x \log (-4+x)}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx+\frac {3}{4} \int \frac {e^x x}{(-4+x)^{\frac {1}{x}}+x} \, dx-\frac {3}{4} \int \frac {e^x x^2}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx+\frac {5}{4} \int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx-\frac {5}{4} \int \frac {e^x x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-4 \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-4 \int \frac {\int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx}{-4+x} \, dx+5 \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-16 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+20 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\frac {4 \int e^{\frac {1}{8} (4+4 x)^2} \, dx}{e^2}-\log (-4+x) \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\int \frac {e^x x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\int \frac {e^x \log (-4+x)}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx+\int \frac {e^x \log (-4+x)}{x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx+\int \left (\frac {\int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx}{-4+x}+\frac {4 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx}{-4+x}\right ) \, dx\\ &=6 x-e^{4 x+2 x^2} x-\frac {1}{4} \int \frac {e^x x^2}{(-4+x)^{\frac {1}{x}}+x} \, dx+\frac {1}{4} \int \left (\frac {16 e^x}{(-4+x)^{\frac {1}{x}}+x}+\frac {64 e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}+\frac {4 e^x x}{(-4+x)^{\frac {1}{x}}+x}+\frac {e^x x^2}{(-4+x)^{\frac {1}{x}}+x}\right ) \, dx+\frac {1}{4} \int \frac {\int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx}{-4+x} \, dx-\frac {1}{4} \int \frac {\int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx+4 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx}{-4+x} \, dx+\frac {3}{4} \int \frac {e^x x}{(-4+x)^{\frac {1}{x}}+x} \, dx-\frac {3}{4} \int \left (\frac {4 e^x}{(-4+x)^{\frac {1}{x}}+x}+\frac {16 e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}+\frac {e^x x}{(-4+x)^{\frac {1}{x}}+x}\right ) \, dx+\frac {5}{4} \int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx-\frac {5}{4} \int \left (\frac {e^x}{(-4+x)^{\frac {1}{x}}+x}+\frac {4 e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )}\right ) \, dx-4 \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+5 \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-16 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+20 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\log (-4+x) \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+\log (-4+x) \int \frac {e^x}{x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-\int \frac {e^x x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+\int \frac {\int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx}{-4+x} \, dx+\int \frac {\int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx}{-4+x} \, dx-\int \frac {\int \frac {e^x}{x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx}{-4+x} \, dx\\ &=6 x-e^{4 x+2 x^2} x+\frac {1}{4} \int \frac {\int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx}{-4+x} \, dx-\frac {1}{4} \int \left (\frac {\int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx}{-4+x}+\frac {4 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx}{-4+x}\right ) \, dx-3 \int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx-4 \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+4 \int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx+5 \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-5 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-12 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-16 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+16 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx+20 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\log (-4+x) \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+\log (-4+x) \int \frac {e^x}{x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-\int \frac {e^x x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+\int \frac {e^x x}{(-4+x)^{\frac {1}{x}}+x} \, dx+\int \frac {\int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx}{-4+x} \, dx+\int \frac {\int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx}{-4+x} \, dx-\int \frac {\int \frac {e^x}{x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx}{-4+x} \, dx\\ &=6 x-e^{4 x+2 x^2} x-3 \int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx-4 \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+4 \int \frac {e^x}{(-4+x)^{\frac {1}{x}}+x} \, dx+5 \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-5 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-12 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-16 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+16 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx+20 \int \frac {e^x}{(-4+x) \left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx-\log (-4+x) \int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+\log (-4+x) \int \frac {e^x}{x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx-\int \frac {e^x x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx+\int \frac {e^x x}{(-4+x)^{\frac {1}{x}}+x} \, dx+\int \frac {\int \frac {e^x}{\left ((-4+x)^{\frac {1}{x}}+x\right )^2} \, dx}{-4+x} \, dx-\int \frac {\int \frac {e^x}{x \left ((-4+x)^{\frac {1}{x}}+x\right )} \, dx}{-4+x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 29, normalized size = 1.00 \begin {gather*} x \left (6-e^{2 x (2+x)}+\frac {e^x}{(-4+x)^{\frac {1}{x}}+x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-24*x^3 + 6*x^4 + E^x*(-4*x^3 + x^4) + E^(4*x + 2*x^2)*(4*x^3 + 15*x^4 + 12*x^5 - 4*x^6) + (-4 + x)
^(2/x)*(-24*x + 6*x^2 + E^(4*x + 2*x^2)*(4*x + 15*x^2 + 12*x^3 - 4*x^4)) + (-4 + x)^x^(-1)*(-48*x^2 + 12*x^3 +
E^x*(-5*x - 3*x^2 + x^3) + E^(4*x + 2*x^2)*(8*x^2 + 30*x^3 + 24*x^4 - 8*x^5) + E^x*(-4 + x)*Log[-4 + x]))/(-4
*x^3 + x^4 + (-4 + x)^(2/x)*(-4*x + x^2) + (-4 + x)^x^(-1)*(-8*x^2 + 2*x^3)),x]

[Out]

x*(6 - E^(2*x*(2 + x)) + E^x/((-4 + x)^x^(-1) + x))

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fricas [B]  time = 0.53, size = 62, normalized size = 2.14 \begin {gather*} -\frac {x^{2} e^{\left (2 \, x^{2} + 4 \, x\right )} + {\left (x e^{\left (2 \, x^{2} + 4 \, x\right )} - 6 \, x\right )} {\left (x - 4\right )}^{\left (\frac {1}{x}\right )} - 6 \, x^{2} - x e^{x}}{{\left (x - 4\right )}^{\left (\frac {1}{x}\right )} + x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^4+12*x^3+15*x^2+4*x)*exp(x^2+2*x)^2+6*x^2-24*x)*exp(log(x-4)/x)^2+((x-4)*exp(x)*log(x-4)+(-8
*x^5+24*x^4+30*x^3+8*x^2)*exp(x^2+2*x)^2+(x^3-3*x^2-5*x)*exp(x)+12*x^3-48*x^2)*exp(log(x-4)/x)+(-4*x^6+12*x^5+
15*x^4+4*x^3)*exp(x^2+2*x)^2+(x^4-4*x^3)*exp(x)+6*x^4-24*x^3)/((x^2-4*x)*exp(log(x-4)/x)^2+(2*x^3-8*x^2)*exp(l
og(x-4)/x)+x^4-4*x^3),x, algorithm="fricas")

[Out]

-(x^2*e^(2*x^2 + 4*x) + (x*e^(2*x^2 + 4*x) - 6*x)*(x - 4)^(1/x) - 6*x^2 - x*e^x)/((x - 4)^(1/x) + x)

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giac [B]  time = 1.86, size = 6706, normalized size = 231.24 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^4+12*x^3+15*x^2+4*x)*exp(x^2+2*x)^2+6*x^2-24*x)*exp(log(x-4)/x)^2+((x-4)*exp(x)*log(x-4)+(-8
*x^5+24*x^4+30*x^3+8*x^2)*exp(x^2+2*x)^2+(x^3-3*x^2-5*x)*exp(x)+12*x^3-48*x^2)*exp(log(x-4)/x)+(-4*x^6+12*x^5+
15*x^4+4*x^3)*exp(x^2+2*x)^2+(x^4-4*x^3)*exp(x)+6*x^4-24*x^3)/((x^2-4*x)*exp(log(x-4)/x)^2+(2*x^3-8*x^2)*exp(l
og(x-4)/x)+x^4-4*x^3),x, algorithm="giac")

[Out]

-(x - 4)^((x - 4)/x)*(x - 4)^(5/x)*(x - 4)^4*e^(2*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x - 4)/x + 48)/((x - 4)^(
1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x
- 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4
)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + (x - 4)^(1/x)*(x - 4)^5*e^((x - 4)^2
/x + 4*(x - 4)/x + 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3
+ 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x
- 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - (x -
4)^(1/x)*(x - 4)^5*e^x/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^
3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*
(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - (x
- 4)^((x - 4)/x)*(x - 4)^(5/x)*(x - 4)^3*e^(2*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x - 4)/x + 48)*log(x - 4)/((
x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4
)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 +
8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 6*(x - 4)^(1/x)*(x - 4)^5/((
x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4
)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 +
8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - (x - 4)^((x - 4)/x)*(x - 4)^
(6/x)*(x - 4)^3*e^(2*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x - 4)/x + 48)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x
)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x -
4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)
^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - 11*(x - 4)^((x - 4)/x)*(x - 4)^(5/x)*(x - 4)^3*e^(2*(x - 4)^3/x +
28*(x - 4)^2/x + 80*(x - 4)/x + 48)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(
2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*lo
g(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*
(x - 4)) + 13*(x - 4)^(1/x)*(x - 4)^4*e^((x - 4)^2/x + 4*(x - 4)/x + 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/
x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x
- 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4
)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - 12*(x - 4)^(1/x)*(x - 4)^4*e^x/((x - 4)^(1/x)*(x - 4)^4 + (x - 4
)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*l
og(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(
x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 6*(x - 4)^(1/x)*(x - 4)^4*log(x - 4)/((x - 4)^(1/x)*(x - 4)
^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*
(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x -
4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - (x - 4)^((x - 4)/x)*(x - 4)^(6/x)*(x - 4)^2*e^(2
*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x - 4)/x + 48)*log(x - 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)
^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(
x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x
- 4) - 16*(x - 4)^(1/x)*(x - 4)) - 8*(x - 4)^((x - 4)/x)*(x - 4)^(5/x)*(x - 4)^2*e^(2*(x - 4)^3/x + 28*(x - 4
)^2/x + 80*(x - 4)/x + 48)*log(x - 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^
(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*l
og(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)
*(x - 4)) + (x - 4)^(1/x)*(x - 4)^3*e^((x - 4)^2/x + 4*(x - 4)/x + 4)*log(x - 4)/((x - 4)^(1/x)*(x - 4)^4 + (x
- 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)
^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 -
4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 6*(x - 4)^(2/x)*(x - 4)^4/((x - 4)^(1/x)*(x - 4)^4 + (x
- 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)
^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 -
4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 42*(x - 4)^(1/x)*(x - 4)^4/((x - 4)^(1/x)*(x - 4)^4 + (
x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4
)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2
- 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - 7*(x - 4)^((x - 4)/x)*(x - 4)^(6/x)*(x - 4)^2*e^(2*(x
- 4)^3/x + 28*(x - 4)^2/x + 80*(x - 4)/x + 48)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) +
(x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x
- 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x -
4)^(1/x)*(x - 4)) - 36*(x - 4)^((x - 4)/x)*(x - 4)^(5/x)*(x - 4)^2*e^(2*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x
- 4)/x + 48)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x -
4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/
x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 55*(x - 4)^(1
/x)*(x - 4)^3*e^((x - 4)^2/x + 4*(x - 4)/x + 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4)
+ (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(
x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x
- 4)^(1/x)*(x - 4)) - 48*(x - 4)^(1/x)*(x - 4)^3*e^x/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x
- 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1
/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 1
6*(x - 4)^(1/x)*(x - 4)) + 6*(x - 4)^(2/x)*(x - 4)^3*log(x - 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x -
4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4
*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*
(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 24*(x - 4)^(1/x)*(x - 4)^3*log(x - 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)
^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*lo
g(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x
- 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - 4*(x - 4)^((x - 4)/x)*(x - 4)^(6/x)*(x - 4)*e^(2*(x - 4)^3/x
+ 28*(x - 4)^2/x + 80*(x - 4)/x + 48)*log(x - 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4
) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)
*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(
x - 4)^(1/x)*(x - 4)) - 16*(x - 4)^((x - 4)/x)*(x - 4)^(5/x)*(x - 4)*e^(2*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x
- 4)/x + 48)*log(x - 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)
^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3
*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 4
*(x - 4)^(1/x)*(x - 4)^2*e^((x - 4)^2/x + 4*(x - 4)/x + 4)*log(x - 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)
*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x -
4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^
(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 18*(x - 4)^(2/x)*(x - 4)^3/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x
)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x -
4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)
^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 48*(x - 4)^(1/x)*(x - 4)^3/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/
x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x
- 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4
)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - 8*(x - 4)^((x - 4)/x)*(x - 4)^(6/x)*(x - 4)*e^(2*(x - 4)^3/x + 2
8*(x - 4)^2/x + 80*(x - 4)/x + 48)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/
x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(
x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x
- 4)) - 16*(x - 4)^((x - 4)/x)*(x - 4)^(5/x)*(x - 4)*e^(2*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x - 4)/x + 48)/(
(x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x -
4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 +
8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 72*(x - 4)^(1/x)*(x - 4)^2*
e^((x - 4)^2/x + 4*(x - 4)/x + 4)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x
)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x
- 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x
- 4)) - 64*(x - 4)^(1/x)*(x - 4)^2*e^x/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)
^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*
log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x
)*(x - 4)) - 24*(x - 4)^(2/x)*(x - 4)^2/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4
)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2
*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/
x)*(x - 4)) - 96*(x - 4)^(1/x)*(x - 4)^2/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x -
4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^
2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1
/x)*(x - 4)) + 16*(x - 4)^((x - 4)/x)*(x - 4)^(6/x)*e^(2*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x - 4)/x + 48)/((x
- 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)
^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8
*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4)) + 64*(x - 4)^((x - 4)/x)*(x - 4
)^(5/x)*e^(2*(x - 4)^3/x + 28*(x - 4)^2/x + 80*(x - 4)/x + 48)/((x - 4)^(1/x)*(x - 4)^4 + (x - 4)^(1/x)*(x - 4
)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4)^(2/x)*(x - 4)^2*log(x - 4) + 4*
(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(
x - 4) - 16*(x - 4)^(1/x)*(x - 4)) - 16*(x - 4)^(1/x)*(x - 4)*e^((x - 4)^2/x + 4*(x - 4)/x + 4)/((x - 4)^(1/x)
*(x - 4)^4 + (x - 4)^(1/x)*(x - 4)^3*log(x - 4) + (x - 4)^(2/x)*(x - 4)^3 + 7*(x - 4)^(1/x)*(x - 4)^3 + (x - 4
)^(2/x)*(x - 4)^2*log(x - 4) + 4*(x - 4)^(1/x)*(x - 4)^2*log(x - 4) + 3*(x - 4)^(2/x)*(x - 4)^2 + 8*(x - 4)^(1
/x)*(x - 4)^2 - 4*(x - 4)^(2/x)*(x - 4) - 16*(x - 4)^(1/x)*(x - 4))

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maple [A]  time = 0.26, size = 30, normalized size = 1.03

method	result	size
risch	\(-x \,{\mathrm e}^{2 x \left (2+x \right )}+6 x +\frac {{\mathrm e}^{x} x}{\left (x -4\right )^{\frac {1}{x}}+x}\)	\(30\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x^4+12*x^3+15*x^2+4*x)*exp(x^2+2*x)^2+6*x^2-24*x)*exp(ln(x-4)/x)^2+((x-4)*exp(x)*ln(x-4)+(-8*x^5+24*
x^4+30*x^3+8*x^2)*exp(x^2+2*x)^2+(x^3-3*x^2-5*x)*exp(x)+12*x^3-48*x^2)*exp(ln(x-4)/x)+(-4*x^6+12*x^5+15*x^4+4*
x^3)*exp(x^2+2*x)^2+(x^4-4*x^3)*exp(x)+6*x^4-24*x^3)/((x^2-4*x)*exp(ln(x-4)/x)^2+(2*x^3-8*x^2)*exp(ln(x-4)/x)+
x^4-4*x^3),x,method=_RETURNVERBOSE)

[Out]

-x*exp(2*x*(2+x))+6*x+exp(x)*x/((x-4)^(1/x)+x)

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maxima [B]  time = 0.48, size = 62, normalized size = 2.14 \begin {gather*} -\frac {x^{2} e^{\left (2 \, x^{2} + 4 \, x\right )} + {\left (x e^{\left (2 \, x^{2} + 4 \, x\right )} - 6 \, x\right )} {\left (x - 4\right )}^{\left (\frac {1}{x}\right )} - 6 \, x^{2} - x e^{x}}{{\left (x - 4\right )}^{\left (\frac {1}{x}\right )} + x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^4+12*x^3+15*x^2+4*x)*exp(x^2+2*x)^2+6*x^2-24*x)*exp(log(x-4)/x)^2+((x-4)*exp(x)*log(x-4)+(-8
*x^5+24*x^4+30*x^3+8*x^2)*exp(x^2+2*x)^2+(x^3-3*x^2-5*x)*exp(x)+12*x^3-48*x^2)*exp(log(x-4)/x)+(-4*x^6+12*x^5+
15*x^4+4*x^3)*exp(x^2+2*x)^2+(x^4-4*x^3)*exp(x)+6*x^4-24*x^3)/((x^2-4*x)*exp(log(x-4)/x)^2+(2*x^3-8*x^2)*exp(l
og(x-4)/x)+x^4-4*x^3),x, algorithm="maxima")

[Out]

-(x^2*e^(2*x^2 + 4*x) + (x*e^(2*x^2 + 4*x) - 6*x)*(x - 4)^(1/x) - 6*x^2 - x*e^x)/((x - 4)^(1/x) + x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{2\,x^2+4\,x}\,\left (-4\,x^6+12\,x^5+15\,x^4+4\,x^3\right )-{\mathrm {e}}^x\,\left (4\,x^3-x^4\right )+{\mathrm {e}}^{\frac {\ln \left (x-4\right )}{x}}\,\left ({\mathrm {e}}^{2\,x^2+4\,x}\,\left (-8\,x^5+24\,x^4+30\,x^3+8\,x^2\right )-48\,x^2+12\,x^3-{\mathrm {e}}^x\,\left (-x^3+3\,x^2+5\,x\right )+\ln \left (x-4\right )\,{\mathrm {e}}^x\,\left (x-4\right )\right )+{\mathrm {e}}^{\frac {2\,\ln \left (x-4\right )}{x}}\,\left ({\mathrm {e}}^{2\,x^2+4\,x}\,\left (-4\,x^4+12\,x^3+15\,x^2+4\,x\right )-24\,x+6\,x^2\right )-24\,x^3+6\,x^4}{{\mathrm {e}}^{\frac {\ln \left (x-4\right )}{x}}\,\left (8\,x^2-2\,x^3\right )+{\mathrm {e}}^{\frac {2\,\ln \left (x-4\right )}{x}}\,\left (4\,x-x^2\right )+4\,x^3-x^4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(4*x + 2*x^2)*(4*x^3 + 15*x^4 + 12*x^5 - 4*x^6) - exp(x)*(4*x^3 - x^4) + exp(log(x - 4)/x)*(exp(4*x +
2*x^2)*(8*x^2 + 30*x^3 + 24*x^4 - 8*x^5) - 48*x^2 + 12*x^3 - exp(x)*(5*x + 3*x^2 - x^3) + log(x - 4)*exp(x)*(
x - 4)) + exp((2*log(x - 4))/x)*(exp(4*x + 2*x^2)*(4*x + 15*x^2 + 12*x^3 - 4*x^4) - 24*x + 6*x^2) - 24*x^3 + 6
*x^4)/(exp(log(x - 4)/x)*(8*x^2 - 2*x^3) + exp((2*log(x - 4))/x)*(4*x - x^2) + 4*x^3 - x^4),x)

[Out]

int(-(exp(4*x + 2*x^2)*(4*x^3 + 15*x^4 + 12*x^5 - 4*x^6) - exp(x)*(4*x^3 - x^4) + exp(log(x - 4)/x)*(exp(4*x +
2*x^2)*(8*x^2 + 30*x^3 + 24*x^4 - 8*x^5) - 48*x^2 + 12*x^3 - exp(x)*(5*x + 3*x^2 - x^3) + log(x - 4)*exp(x)*(
x - 4)) + exp((2*log(x - 4))/x)*(exp(4*x + 2*x^2)*(4*x + 15*x^2 + 12*x^3 - 4*x^4) - 24*x + 6*x^2) - 24*x^3 + 6
*x^4)/(exp(log(x - 4)/x)*(8*x^2 - 2*x^3) + exp((2*log(x - 4))/x)*(4*x - x^2) + 4*x^3 - x^4), x)

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sympy [A]  time = 1.62, size = 29, normalized size = 1.00 \begin {gather*} - x e^{2 x^{2} + 4 x} + 6 x + \frac {x e^{x}}{x + e^{\frac {\log {\left (x - 4 \right )}}{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x**4+12*x**3+15*x**2+4*x)*exp(x**2+2*x)**2+6*x**2-24*x)*exp(ln(x-4)/x)**2+((x-4)*exp(x)*ln(x-4
)+(-8*x**5+24*x**4+30*x**3+8*x**2)*exp(x**2+2*x)**2+(x**3-3*x**2-5*x)*exp(x)+12*x**3-48*x**2)*exp(ln(x-4)/x)+(
-4*x**6+12*x**5+15*x**4+4*x**3)*exp(x**2+2*x)**2+(x**4-4*x**3)*exp(x)+6*x**4-24*x**3)/((x**2-4*x)*exp(ln(x-4)/
x)**2+(2*x**3-8*x**2)*exp(ln(x-4)/x)+x**4-4*x**3),x)

[Out]

-x*exp(2*x**2 + 4*x) + 6*x + x*exp(x)/(x + exp(log(x - 4)/x))

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