3.83.8 \(\int \frac {-2 x^2-2 x^3+x^{2/x} (4+4 x+(-4-4 x) \log (x))+x^{\frac {1}{x}} (-16-16 x+(16+16 x) \log (x))+(13 x^2-x^3-8 x^{2+\frac {1}{x}}+x^{2+\frac {2}{x}}) \log (169-26 x+x^2+(90-2 x) x^{2/x}-16 x^{3/x}+x^{4/x}+x^{\frac {1}{x}} (-208+16 x))}{13 x^2-x^3-8 x^{2+\frac {1}{x}}+x^{2+\frac {2}{x}}} \, dx\)

Optimal. Leaf size=23 \[ (1+x) \log \left (\left (3+x-\left (4-x^{\frac {1}{x}}\right )^2\right )^2\right ) \]

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Rubi [F]  time = 4.78, 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 {-2 x^2-2 x^3+x^{2/x} (4+4 x+(-4-4 x) \log (x))+x^{\frac {1}{x}} (-16-16 x+(16+16 x) \log (x))+\left (13 x^2-x^3-8 x^{2+\frac {1}{x}}+x^{2+\frac {2}{x}}\right ) \log \left (169-26 x+x^2+(90-2 x) x^{2/x}-16 x^{3/x}+x^{4/x}+x^{\frac {1}{x}} (-208+16 x)\right )}{13 x^2-x^3-8 x^{2+\frac {1}{x}}+x^{2+\frac {2}{x}}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2*x^2 - 2*x^3 + x^(2/x)*(4 + 4*x + (-4 - 4*x)*Log[x]) + x^x^(-1)*(-16 - 16*x + (16 + 16*x)*Log[x]) + (13
*x^2 - x^3 - 8*x^(2 + x^(-1)) + x^(2 + 2/x))*Log[169 - 26*x + x^2 + (90 - 2*x)*x^(2/x) - 16*x^(3/x) + x^(4/x)
+ x^x^(-1)*(-208 + 16*x)])/(13*x^2 - x^3 - 8*x^(2 + x^(-1)) + x^(2 + 2/x)),x]

[Out]

4/x + 2*(1 - Log[x])^2 - 4*(1 - Log[x])*(x^(-1) - Log[x]) + 2*Log[x]^2 + x*Log[(13 - x - 8*x^x^(-1) + x^(2/x))
^2] - 2*Defer[Int][(13 - x - 8*x^x^(-1) + x^(2/x))^(-1), x] - 52*Defer[Int][1/(x^2*(13 - x - 8*x^x^(-1) + x^(2
/x))), x] + 52*Log[x]*Defer[Int][1/(x^2*(13 - x - 8*x^x^(-1) + x^(2/x))), x] + 4*Defer[Int][1/(x*(13 - x - 8*x
^x^(-1) + x^(2/x))), x] - 4*Log[x]*Defer[Int][1/(x*(13 - x - 8*x^x^(-1) + x^(2/x))), x] + 16*Defer[Int][x^(-2
+ x^(-1))/(13 - x - 8*x^x^(-1) + x^(2/x)), x] - 16*Log[x]*Defer[Int][x^(-2 + x^(-1))/(13 - x - 8*x^x^(-1) + x^
(2/x)), x] - 52*Defer[Int][Defer[Int][1/(x^2*(13 - x - 8*x^x^(-1) + x^(2/x))), x]/x, x] + 4*Defer[Int][Defer[I
nt][1/(x*(13 - x - 8*x^x^(-1) + x^(2/x))), x]/x, x] + 16*Defer[Int][Defer[Int][x^(-2 + x^(-1))/(13 - x - 8*x^x
^(-1) + x^(2/x)), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 x^2-2 x^3+16 x^{\frac {1}{x}} (1+x) (-1+\log (x))-4 x^{2/x} (1+x) (-1+\log (x))-x^2 \left (-13+x+8 x^{\frac {1}{x}}-x^{2/x}\right ) \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right )}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx\\ &=\int \left (-\frac {2 (1+x) \left (26-2 x+x^2-8 x^{\frac {1}{x}}-26 \log (x)+2 x \log (x)+8 x^{\frac {1}{x}} \log (x)\right )}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}+\frac {4+4 x-4 \log (x)-4 x \log (x)+x^2 \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right )}{x^2}\right ) \, dx\\ &=-\left (2 \int \frac {(1+x) \left (26-2 x+x^2-8 x^{\frac {1}{x}}-26 \log (x)+2 x \log (x)+8 x^{\frac {1}{x}} \log (x)\right )}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx\right )+\int \frac {4+4 x-4 \log (x)-4 x \log (x)+x^2 \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right )}{x^2} \, dx\\ &=-\left (2 \int \left (\frac {26-2 x+x^2-8 x^{\frac {1}{x}}-26 \log (x)+2 x \log (x)+8 x^{\frac {1}{x}} \log (x)}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}+\frac {26-2 x+x^2-8 x^{\frac {1}{x}}-26 \log (x)+2 x \log (x)+8 x^{\frac {1}{x}} \log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}\right ) \, dx\right )+\int \left (-\frac {4 (1+x) (-1+\log (x))}{x^2}+\log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right )\right ) \, dx\\ &=-\left (2 \int \frac {26-2 x+x^2-8 x^{\frac {1}{x}}-26 \log (x)+2 x \log (x)+8 x^{\frac {1}{x}} \log (x)}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx\right )-2 \int \frac {26-2 x+x^2-8 x^{\frac {1}{x}}-26 \log (x)+2 x \log (x)+8 x^{\frac {1}{x}} \log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-4 \int \frac {(1+x) (-1+\log (x))}{x^2} \, dx+\int \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right ) \, dx\\ &=-4 (1-\log (x)) \left (\frac {1}{x}-\log (x)\right )+x \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right )-2 \int \left (\frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}}+\frac {26}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}-\frac {2}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}-\frac {8 x^{-2+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}}-\frac {26 \log (x)}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}+\frac {2 \log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}+\frac {8 x^{-2+\frac {1}{x}} \log (x)}{13-x-8 x^{\frac {1}{x}}+x^{2/x}}\right ) \, dx-2 \int \left (-\frac {2}{13-x-8 x^{\frac {1}{x}}+x^{2/x}}+\frac {26}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}+\frac {x}{13-x-8 x^{\frac {1}{x}}+x^{2/x}}-\frac {8 x^{-1+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}}+\frac {2 \log (x)}{13-x-8 x^{\frac {1}{x}}+x^{2/x}}-\frac {26 \log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}+\frac {8 x^{-1+\frac {1}{x}} \log (x)}{13-x-8 x^{\frac {1}{x}}+x^{2/x}}\right ) \, dx+4 \int \frac {-1+x \log (x)}{x^2} \, dx-\int \frac {2 \left (-x^2-8 x^{\frac {1}{x}}+2 x^{2/x}-2 x^{\frac {1}{x}} \left (-4+x^{\frac {1}{x}}\right ) \log (x)\right )}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx\\ &=-4 (1-\log (x)) \left (\frac {1}{x}-\log (x)\right )+x \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right )-2 \int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-2 \int \frac {x}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-2 \int \frac {-x^2-8 x^{\frac {1}{x}}+2 x^{2/x}-2 x^{\frac {1}{x}} \left (-4+x^{\frac {1}{x}}\right ) \log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+4 \int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+4 \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-4 \int \frac {\log (x)}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-4 \int \frac {\log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+4 \int \left (-\frac {1}{x^2}+\frac {\log (x)}{x}\right ) \, dx+16 \int \frac {x^{-2+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+16 \int \frac {x^{-1+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-16 \int \frac {x^{-2+\frac {1}{x}} \log (x)}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-16 \int \frac {x^{-1+\frac {1}{x}} \log (x)}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-52 \int \frac {1}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-52 \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+52 \int \frac {\log (x)}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+52 \int \frac {\log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx\\ &=\frac {4}{x}-4 (1-\log (x)) \left (\frac {1}{x}-\log (x)\right )+x \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right )-2 \int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-2 \int \frac {x}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-2 \int \left (-\frac {2 (-1+\log (x))}{x}-\frac {26-2 x+x^2-8 x^{\frac {1}{x}}-26 \log (x)+2 x \log (x)+8 x^{\frac {1}{x}} \log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )}\right ) \, dx+4 \int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+4 \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+4 \int \frac {\log (x)}{x} \, dx+4 \int \frac {\int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx}{x} \, dx+4 \int \frac {\int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx}{x} \, dx+16 \int \frac {x^{-2+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+16 \int \frac {x^{-1+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+16 \int \frac {\int \frac {x^{-2+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx}{x} \, dx+16 \int \frac {\int \frac {x^{-1+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx}{x} \, dx-52 \int \frac {1}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-52 \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-52 \int \frac {\int \frac {1}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx}{x} \, dx-52 \int \frac {\int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx}{x} \, dx-(4 \log (x)) \int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-(4 \log (x)) \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-(16 \log (x)) \int \frac {x^{-2+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-(16 \log (x)) \int \frac {x^{-1+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+(52 \log (x)) \int \frac {1}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+(52 \log (x)) \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx\\ &=\frac {4}{x}-4 (1-\log (x)) \left (\frac {1}{x}-\log (x)\right )+2 \log ^2(x)+x \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right )-2 \int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-2 \int \frac {x}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+2 \int \frac {26-2 x+x^2-8 x^{\frac {1}{x}}-26 \log (x)+2 x \log (x)+8 x^{\frac {1}{x}} \log (x)}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+4 \int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+4 \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+4 \int \frac {-1+\log (x)}{x} \, dx+4 \int \frac {\int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx}{x} \, dx+4 \int \frac {\int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx}{x} \, dx+16 \int \frac {x^{-2+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+16 \int \frac {x^{-1+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+16 \int \frac {\int \frac {x^{-2+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx}{x} \, dx+16 \int \frac {\int \frac {x^{-1+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx}{x} \, dx-52 \int \frac {1}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-52 \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-52 \int \frac {\int \frac {1}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx}{x} \, dx-52 \int \frac {\int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx}{x} \, dx-(4 \log (x)) \int \frac {1}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-(4 \log (x)) \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx-(16 \log (x)) \int \frac {x^{-2+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx-(16 \log (x)) \int \frac {x^{-1+\frac {1}{x}}}{13-x-8 x^{\frac {1}{x}}+x^{2/x}} \, dx+(52 \log (x)) \int \frac {1}{x^2 \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx+(52 \log (x)) \int \frac {1}{x \left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.50, size = 47, normalized size = 2.04 \begin {gather*} 2 \log \left (-13+x+8 x^{\frac {1}{x}}-x^{2/x}\right )+x \log \left (\left (13-x-8 x^{\frac {1}{x}}+x^{2/x}\right )^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x^2 - 2*x^3 + x^(2/x)*(4 + 4*x + (-4 - 4*x)*Log[x]) + x^x^(-1)*(-16 - 16*x + (16 + 16*x)*Log[x])
+ (13*x^2 - x^3 - 8*x^(2 + x^(-1)) + x^(2 + 2/x))*Log[169 - 26*x + x^2 + (90 - 2*x)*x^(2/x) - 16*x^(3/x) + x^
(4/x) + x^x^(-1)*(-208 + 16*x)])/(13*x^2 - x^3 - 8*x^(2 + x^(-1)) + x^(2 + 2/x)),x]

[Out]

2*Log[-13 + x + 8*x^x^(-1) - x^(2/x)] + x*Log[(13 - x - 8*x^x^(-1) + x^(2/x))^2]

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fricas [B]  time = 0.56, size = 51, normalized size = 2.22 \begin {gather*} {\left (x + 1\right )} \log \left (-2 \, {\left (x - 45\right )} x^{\frac {2}{x}} + 16 \, {\left (x - 13\right )} x^{\left (\frac {1}{x}\right )} + x^{2} + x^{\frac {4}{x}} - 16 \, x^{\frac {3}{x}} - 26 \, x + 169\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2*exp(log(x)/x)^2-8*x^2*exp(log(x)/x)-x^3+13*x^2)*log(exp(log(x)/x)^4-16*exp(log(x)/x)^3+(-2*x+9
0)*exp(log(x)/x)^2+(16*x-208)*exp(log(x)/x)+x^2-26*x+169)+((-4*x-4)*log(x)+4*x+4)*exp(log(x)/x)^2+((16*x+16)*l
og(x)-16*x-16)*exp(log(x)/x)-2*x^3-2*x^2)/(x^2*exp(log(x)/x)^2-8*x^2*exp(log(x)/x)-x^3+13*x^2),x, algorithm="f
ricas")

[Out]

(x + 1)*log(-2*(x - 45)*x^(2/x) + 16*(x - 13)*x^(1/x) + x^2 + x^(4/x) - 16*x^(3/x) - 26*x + 169)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2*exp(log(x)/x)^2-8*x^2*exp(log(x)/x)-x^3+13*x^2)*log(exp(log(x)/x)^4-16*exp(log(x)/x)^3+(-2*x+9
0)*exp(log(x)/x)^2+(16*x-208)*exp(log(x)/x)+x^2-26*x+169)+((-4*x-4)*log(x)+4*x+4)*exp(log(x)/x)^2+((16*x+16)*l
og(x)-16*x-16)*exp(log(x)/x)-2*x^3-2*x^2)/(x^2*exp(log(x)/x)^2-8*x^2*exp(log(x)/x)-x^3+13*x^2),x, algorithm="g
iac")

[Out]

undef

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maple [C]  time = 0.21, size = 189, normalized size = 8.22

method	result	size
risch	\(2 x \ln \left (-x^{\frac {2}{x}}+8 x^{\frac {1}{x}}+x -13\right )-\frac {i \pi x \mathrm {csgn}\left (i \left (-x^{\frac {2}{x}}+8 x^{\frac {1}{x}}+x -13\right )\right )^{2} \mathrm {csgn}\left (i \left (-x^{\frac {2}{x}}+8 x^{\frac {1}{x}}+x -13\right )^{2}\right )}{2}+i \pi x \,\mathrm {csgn}\left (i \left (-x^{\frac {2}{x}}+8 x^{\frac {1}{x}}+x -13\right )\right ) \mathrm {csgn}\left (i \left (-x^{\frac {2}{x}}+8 x^{\frac {1}{x}}+x -13\right )^{2}\right )^{2}-\frac {i \pi x \mathrm {csgn}\left (i \left (-x^{\frac {2}{x}}+8 x^{\frac {1}{x}}+x -13\right )^{2}\right )^{3}}{2}+2 \ln \left (x^{\frac {2}{x}}-8 x^{\frac {1}{x}}-x +13\right )\)	\(189\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^2*exp(ln(x)/x)^2-8*x^2*exp(ln(x)/x)-x^3+13*x^2)*ln(exp(ln(x)/x)^4-16*exp(ln(x)/x)^3+(-2*x+90)*exp(ln(x
)/x)^2+(16*x-208)*exp(ln(x)/x)+x^2-26*x+169)+((-4*x-4)*ln(x)+4*x+4)*exp(ln(x)/x)^2+((16*x+16)*ln(x)-16*x-16)*e
xp(ln(x)/x)-2*x^3-2*x^2)/(x^2*exp(ln(x)/x)^2-8*x^2*exp(ln(x)/x)-x^3+13*x^2),x,method=_RETURNVERBOSE)

[Out]

2*x*ln(-(x^(1/x))^2+8*x^(1/x)+x-13)-1/2*I*Pi*x*csgn(I*(-(x^(1/x))^2+8*x^(1/x)+x-13))^2*csgn(I*(-(x^(1/x))^2+8*
x^(1/x)+x-13)^2)+I*Pi*x*csgn(I*(-(x^(1/x))^2+8*x^(1/x)+x-13))*csgn(I*(-(x^(1/x))^2+8*x^(1/x)+x-13)^2)^2-1/2*I*
Pi*x*csgn(I*(-(x^(1/x))^2+8*x^(1/x)+x-13)^2)^3+2*ln((x^(1/x))^2-8*x^(1/x)-x+13)

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maxima [A]  time = 0.41, size = 25, normalized size = 1.09 \begin {gather*} 2 \, {\left (x + 1\right )} \log \left (x^{\frac {2}{x}} - x - 8 \, x^{\left (\frac {1}{x}\right )} + 13\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2*exp(log(x)/x)^2-8*x^2*exp(log(x)/x)-x^3+13*x^2)*log(exp(log(x)/x)^4-16*exp(log(x)/x)^3+(-2*x+9
0)*exp(log(x)/x)^2+(16*x-208)*exp(log(x)/x)+x^2-26*x+169)+((-4*x-4)*log(x)+4*x+4)*exp(log(x)/x)^2+((16*x+16)*l
og(x)-16*x-16)*exp(log(x)/x)-2*x^3-2*x^2)/(x^2*exp(log(x)/x)^2-8*x^2*exp(log(x)/x)-x^3+13*x^2),x, algorithm="m
axima")

[Out]

2*(x + 1)*log(x^(2/x) - x - 8*x^(1/x) + 13)

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mupad [B]  time = 6.48, size = 84, normalized size = 3.65 \begin {gather*} 2\,\ln \left (x-x^{2/x}+8\,x^{1/x}-13\right )+x\,\ln \left (90\,x^{2/x}-26\,x-16\,x^{3/x}+x^{4/x}+16\,x\,x^{1/x}-208\,x^{1/x}+x^2-2\,x\,x^{2/x}+169\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(exp((4*log(x))/x) - 16*exp((3*log(x))/x) - 26*x - exp((2*log(x))/x)*(2*x - 90) + exp(log(x)/x)*(16*x
- 208) + x^2 + 169)*(8*x^2*exp(log(x)/x) - x^2*exp((2*log(x))/x) - 13*x^2 + x^3) - exp((2*log(x))/x)*(4*x - lo
g(x)*(4*x + 4) + 4) + exp(log(x)/x)*(16*x - log(x)*(16*x + 16) + 16) + 2*x^2 + 2*x^3)/(8*x^2*exp(log(x)/x) - x
^2*exp((2*log(x))/x) - 13*x^2 + x^3),x)

[Out]

2*log(x - x^(2/x) + 8*x^(1/x) - 13) + x*log(90*x^(2/x) - 26*x - 16*x^(3/x) + x^(4/x) + 16*x*x^(1/x) - 208*x^(1
/x) + x^2 - 2*x*x^(2/x) + 169)

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sympy [B]  time = 3.45, size = 78, normalized size = 3.39 \begin {gather*} x \log {\left (x^{2} - 26 x + \left (90 - 2 x\right ) e^{\frac {2 \log {\relax (x )}}{x}} + \left (16 x - 208\right ) e^{\frac {\log {\relax (x )}}{x}} + e^{\frac {4 \log {\relax (x )}}{x}} - 16 e^{\frac {3 \log {\relax (x )}}{x}} + 169 \right )} + 2 \log {\left (- x + e^{\frac {2 \log {\relax (x )}}{x}} - 8 e^{\frac {\log {\relax (x )}}{x}} + 13 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**2*exp(ln(x)/x)**2-8*x**2*exp(ln(x)/x)-x**3+13*x**2)*ln(exp(ln(x)/x)**4-16*exp(ln(x)/x)**3+(-2*x
+90)*exp(ln(x)/x)**2+(16*x-208)*exp(ln(x)/x)+x**2-26*x+169)+((-4*x-4)*ln(x)+4*x+4)*exp(ln(x)/x)**2+((16*x+16)*
ln(x)-16*x-16)*exp(ln(x)/x)-2*x**3-2*x**2)/(x**2*exp(ln(x)/x)**2-8*x**2*exp(ln(x)/x)-x**3+13*x**2),x)

[Out]

x*log(x**2 - 26*x + (90 - 2*x)*exp(2*log(x)/x) + (16*x - 208)*exp(log(x)/x) + exp(4*log(x)/x) - 16*exp(3*log(x
)/x) + 169) + 2*log(-x + exp(2*log(x)/x) - 8*exp(log(x)/x) + 13)

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