3.73.54 $\int \frac{(7x+14e^{2x}x)\log (-\frac{10}{x})+(-7e^{2x}-7x+(-7e^{2x}x-7x^2)\log (-\frac{10}{x}))\log (e^{2x}+x)}{3e^{3x}x+3e^x{x}^2}dx$

Optimal. Leaf size=23 $$\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)$$

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Rubi [F]  time = 4.01, 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 = {} $$\begin{array}{c}\int \frac{(7x+14e^{2x}x)\log (-\frac{10}{x})+(-7e^{2x}-7x+(-7e^{2x}x-7x^2)\log (-\frac{10}{x}))\log (e^{2x}+x)}{3e^{3x}x+3e^x{x}^2}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[((7*x + 14*E^(2*x)*x)*Log[-10/x] + (-7*E^(2*x) - 7*x + (-7*E^(2*x)*x - 7*x^2)*Log[-10/x])*Log[E^(2*x) + x]
)/(3*E^(3*x)*x + 3*E^x*x^2),x]

[Out]

(-14*ExpIntegralEi[-x])/3 + (7*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, -x])/3 - (14*Log[-10/x])/(3*E^x) - (7
*ExpIntegralEi[-x]*Log[-10/x])/3 - (7*EulerGamma*Log[x])/3 - (7*(ExpIntegralE[1, x] + ExpIntegralEi[-x])*Log[x
])/3 - (7*Log[x]^2)/6 + (7*Log[-10/x]*Log[E^(2*x) + x])/(3*E^x) + (7*Log[-10/x]*Defer[Int][1/(E^x*(E^(2*x) + x
)), x])/3 - (14*Log[-10/x]*Defer[Int][E^x/(E^(2*x) + x), x])/3 + (7*Log[-10/x]*Defer[Int][E^x/(x*(E^(2*x) + x)
), x])/3 - (14*Log[-10/x]*Defer[Int][x/(E^x*(E^(2*x) + x)), x])/3 + (7*Defer[Int][Defer[Int][1/(E^x*(E^(2*x) +
x)), x]/x, x])/3 - (14*Defer[Int][Defer[Int][E^x/(E^(2*x) + x), x]/x, x])/3 + (7*Defer[Int][Defer[Int][E^x/(x
*(E^(2*x) + x)), x]/x, x])/3 - (14*Defer[Int][Defer[Int][x/(E^x*(E^(2*x) + x)), x]/x, x])/3

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^{-x}((7x+14e^{2x}x)\log (-\frac{10}{x})+(-7e^{2x}-7x+(-7e^{2x}x-7x^2)\log (-\frac{10}{x}))\log (e^{2x}+x))}{3x(e^{2x}+x)}dx\\ & =\frac{1}{3}\int \frac{e^{-x}((7x+14e^{2x}x)\log (-\frac{10}{x})+(-7e^{2x}-7x+(-7e^{2x}x-7x^2)\log (-\frac{10}{x}))\log (e^{2x}+x))}{x(e^{2x}+x)}dx\\ & =\frac{1}{3}\int (-\frac{7e^{-x}(-1+2x)\log (-\frac{10}{x})}{e^{2x}+x}-\frac{7e^{-x}(-2x\log (-\frac{10}{x})+\log (e^{2x}+x)+x\log (-\frac{10}{x})\log (e^{2x}+x))}{x})dx\\ & =-(\frac{7}{3}\int \frac{e^{-x}(-1+2x)\log (-\frac{10}{x})}{e^{2x}+x}dx)-\frac{7}{3}\int \frac{e^{-x}(-2x\log (-\frac{10}{x})+\log (e^{2x}+x)+x\log (-\frac{10}{x})\log (e^{2x}+x))}{x}dx\\ & =-(\frac{7}{3}\int (-2e^{-x}\log (-\frac{10}{x})+\frac{e^{-x}(1+x\log (-\frac{10}{x}))\log (e^{2x}+x)}{x})dx)-\frac{7}{3}\int \frac{-\int \frac{e^{-x}}{e^{2x}+x}dx+2\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-(\frac{7}{3}\int \frac{e^{-x}(1+x\log (-\frac{10}{x}))\log (e^{2x}+x)}{x}dx)-\frac{7}{3}\int (-\frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}+\frac{2\int \frac{e^{-x}x}{e^{2x}+x}dx}{x})dx+\frac{14}{3}\int e^{-x}\log (-\frac{10}{x})dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\int (\frac{e^{-x}\log (e^{2x}+x)}{x}+e^{-x}\log (-\frac{10}{x})\log (e^{2x}+x))dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx-\frac{14}{3}\int \frac{e^{-x}}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14\text{Ei}(-x)}{3}-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\int \frac{e^{-x}\log (e^{2x}+x)}{x}dx-\frac{7}{3}\int e^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14\text{Ei}(-x)}{3}-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\text{Ei}(-x)\log (e^{2x}+x)+\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)+\frac{7}{3}\int \frac{(1+2e^{2x})\text{Ei}(-x)}{e^{2x}+x}dx-\frac{7}{3}\int \frac{e^{-x}(1+2e^{2x})\log (-\frac{10}{x})}{e^{2x}+x}dx+\frac{7}{3}\int \frac{e^{-x}\log (e^{2x}+x)}{x}dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14\text{Ei}(-x)}{3}-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\text{Ei}(-x)\log (-\frac{10}{x})+\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)-\frac{7}{3}\int \frac{(1+2e^{2x})\text{Ei}(-x)}{e^{2x}+x}dx+\frac{7}{3}\int (2\text{Ei}(-x)-\frac{(-1+2x)\text{Ei}(-x)}{e^{2x}+x})dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx-\frac{7}{3}\int \frac{\text{Ei}(-x)+2\int \frac{e^x}{e^{2x}+x}dx-\int \frac{e^x}{x(e^{2x}+x)}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^x}{x(e^{2x}+x)}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^x}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14\text{Ei}(-x)}{3}-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\text{Ei}(-x)\log (-\frac{10}{x})+\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)-\frac{7}{3}\int \frac{(-1+2x)\text{Ei}(-x)}{e^{2x}+x}dx-\frac{7}{3}\int (2\text{Ei}(-x)-\frac{(-1+2x)\text{Ei}(-x)}{e^{2x}+x})dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx-\frac{7}{3}\int (\frac{\text{Ei}(-x)+2\int \frac{e^x}{e^{2x}+x}dx}{x}-\frac{\int \frac{e^x}{x(e^{2x}+x)}dx}{x})dx+\frac{14\int \text{Ei}(-x)dx}{3}-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^x}{x(e^{2x}+x)}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^x}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =\frac{14e^{-x}}{3}-\frac{14\text{Ei}(-x)}{3}+\frac{14x\text{Ei}(-x)}{3}-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\text{Ei}(-x)\log (-\frac{10}{x})+\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)+\frac{7}{3}\int \frac{(-1+2x)\text{Ei}(-x)}{e^{2x}+x}dx-\frac{7}{3}\int (-\frac{\text{Ei}(-x)}{e^{2x}+x}+\frac{2x\text{Ei}(-x)}{e^{2x}+x})dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx-\frac{7}{3}\int \frac{\text{Ei}(-x)+2\int \frac{e^x}{e^{2x}+x}dx}{x}dx+\frac{7}{3}\int \frac{\int \frac{e^x}{x(e^{2x}+x)}dx}{x}dx-\frac{14\int \text{Ei}(-x)dx}{3}-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^x}{x(e^{2x}+x)}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^x}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14\text{Ei}(-x)}{3}-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\text{Ei}(-x)\log (-\frac{10}{x})+\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)+\frac{7}{3}\int \frac{\text{Ei}(-x)}{e^{2x}+x}dx+\frac{7}{3}\int (-\frac{\text{Ei}(-x)}{e^{2x}+x}+\frac{2x\text{Ei}(-x)}{e^{2x}+x})dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx-\frac{7}{3}\int (\frac{\text{Ei}(-x)}{x}+\frac{2\int \frac{e^x}{e^{2x}+x}dx}{x})dx+\frac{7}{3}\int \frac{\int \frac{e^x}{x(e^{2x}+x)}dx}{x}dx-\frac{14}{3}\int \frac{x\text{Ei}(-x)}{e^{2x}+x}dx-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^x}{x(e^{2x}+x)}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^x}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14\text{Ei}(-x)}{3}-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\text{Ei}(-x)\log (-\frac{10}{x})+\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)-\frac{7}{3}\int \frac{\text{Ei}(-x)}{x}dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx+\frac{7}{3}\int \frac{\int \frac{e^x}{x(e^{2x}+x)}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^x}{e^{2x}+x}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^x}{x(e^{2x}+x)}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^x}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14\text{Ei}(-x)}{3}-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\text{Ei}(-x)\log (-\frac{10}{x})-\frac{7}{3}(E_1(x)+\text{Ei}(-x))\log (x)+\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)+\frac{7}{3}\int \frac{E_1(x)}{x}dx+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx+\frac{7}{3}\int \frac{\int \frac{e^x}{x(e^{2x}+x)}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^x}{e^{2x}+x}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^x}{x(e^{2x}+x)}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^x}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\\ & =-\frac{14\text{Ei}(-x)}{3}+\frac{7}{3}x{}_3{F}_3(1,1,1;2,2,2;-x)-\frac{14}{3}{e}^{-x}\log (-\frac{10}{x})-\frac{7}{3}\text{Ei}(-x)\log (-\frac{10}{x})-\frac{7}{3}\gamma \log (x)-\frac{7}{3}(E_1(x)+\text{Ei}(-x))\log (x)-\frac{7{\log }^2(x)}{6}+\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)+\frac{7}{3}\int \frac{\int \frac{e^{-x}}{e^{2x}+x}dx}{x}dx+\frac{7}{3}\int \frac{\int \frac{e^x}{x(e^{2x}+x)}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^x}{e^{2x}+x}dx}{x}dx-\frac{14}{3}\int \frac{\int \frac{e^{-x}x}{e^{2x}+x}dx}{x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^{-x}}{e^{2x}+x}dx+\frac{1}{3}(7\log (-\frac{10}{x}))\int \frac{e^x}{x(e^{2x}+x)}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^x}{e^{2x}+x}dx-\frac{1}{3}(14\log (-\frac{10}{x}))\int \frac{e^{-x}x}{e^{2x}+x}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.54, size = 23, normalized size = 1.00 $$\begin{array}{c}\frac{7}{3}{e}^{-x}\log (-\frac{10}{x})\log (e^{2x}+x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[((7*x + 14*E^(2*x)*x)*Log[-10/x] + (-7*E^(2*x) - 7*x + (-7*E^(2*x)*x - 7*x^2)*Log[-10/x])*Log[E^(2*x
) + x])/(3*E^(3*x)*x + 3*E^x*x^2),x]

[Out]

(7*Log[-10/x]*Log[E^(2*x) + x])/(3*E^x)

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fricas [A]  time = 0.51, size = 19, normalized size = 0.83 $$\begin{array}{c}\frac{7}{3}{e}^{(-x)}\log (x+e^{\left(2x\right)})\log (-\frac{10}{x})\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-7*x*exp(x)^2-7*x^2)*log(-10/x)-7*exp(x)^2-7*x)*log(exp(x)^2+x)+(14*x*exp(x)^2+7*x)*log(-10/x))/(
3*x*exp(x)^3+3*exp(x)*x^2),x, algorithm="fricas")

[Out]

7/3*e^(-x)*log(x + e^(2*x))*log(-10/x)

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giac [B]  time = 0.16, size = 68, normalized size = 2.96 $$\begin{array}{c}\frac{7}{12}({\pi }^2\mathrm{sgn}(x+e^{\left(2x\right)})\mathrm{sgn}(x)+{\pi }^2\mathrm{sgn}(x+e^{\left(2x\right)})-{\pi }^2\mathrm{sgn}(x)-{\pi }^2+4\log \left(10\right)\log \left(|x+e^{\left(2x\right)}|\right)-4\log \left(|x+e^{\left(2x\right)}|\right)\log \left(\left|x\right|\right))e^{(-x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-7*x*exp(x)^2-7*x^2)*log(-10/x)-7*exp(x)^2-7*x)*log(exp(x)^2+x)+(14*x*exp(x)^2+7*x)*log(-10/x))/(
3*x*exp(x)^3+3*exp(x)*x^2),x, algorithm="giac")

[Out]

7/12*(pi^2*sgn(x + e^(2*x))*sgn(x) + pi^2*sgn(x + e^(2*x)) - pi^2*sgn(x) - pi^2 + 4*log(10)*log(abs(x + e^(2*x
))) - 4*log(abs(x + e^(2*x)))*log(abs(x)))*e^(-x)

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maple [C]  time = 0.12, size = 57, normalized size = 2.48

method	result	size
risch	$\frac{7(-2i\pi \mathrm{csgn}{\left(\frac{i}{x}\right)}^2+2i\pi \mathrm{csgn}{\left(\frac{i}{x}\right)}^3+2i\pi +2\ln (2)+2\ln (5)-2\ln (x)){\mathrm{e}}^{-x}\ln ({\mathrm{e}}^{2x}+x)}{6}$	$57$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-7*x*exp(x)^2-7*x^2)*ln(-10/x)-7*exp(x)^2-7*x)*ln(exp(x)^2+x)+(14*x*exp(x)^2+7*x)*ln(-10/x))/(3*x*exp(x
)^3+3*exp(x)*x^2),x,method=_RETURNVERBOSE)

[Out]

7/6*(-2*I*Pi*csgn(I/x)^2+2*I*Pi*csgn(I/x)^3+2*I*Pi+2*ln(2)+2*ln(5)-2*ln(x))*exp(-x)*ln(exp(2*x)+x)

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maxima [A]  time = 0.48, size = 24, normalized size = 1.04 $$\begin{array}{c}\frac{7}{3}(\log (5)+\log (2)-\log (-x))e^{(-x)}\log (x+e^{\left(2x\right)})\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-7*x*exp(x)^2-7*x^2)*log(-10/x)-7*exp(x)^2-7*x)*log(exp(x)^2+x)+(14*x*exp(x)^2+7*x)*log(-10/x))/(
3*x*exp(x)^3+3*exp(x)*x^2),x, algorithm="maxima")

[Out]

7/3*(log(5) + log(2) - log(-x))*e^(-x)*log(x + e^(2*x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 $$\begin{array}{c}\int \frac{\ln (-\frac{10}{x})(7x+14x{\mathrm{e}}^{2x})-\ln (x+{\mathrm{e}}^{2x})(7x+7{\mathrm{e}}^{2x}+\ln (-\frac{10}{x})(7x{\mathrm{e}}^{2x}+7x^2))}{3x{\mathrm{e}}^{3x}+3x^2{\mathrm{e}}^x}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(-10/x)*(7*x + 14*x*exp(2*x)) - log(x + exp(2*x))*(7*x + 7*exp(2*x) + log(-10/x)*(7*x*exp(2*x) + 7*x^2
)))/(3*x*exp(3*x) + 3*x^2*exp(x)),x)

[Out]

int((log(-10/x)*(7*x + 14*x*exp(2*x)) - log(x + exp(2*x))*(7*x + 7*exp(2*x) + log(-10/x)*(7*x*exp(2*x) + 7*x^2
)))/(3*x*exp(3*x) + 3*x^2*exp(x)), x)

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sympy [A]  time = 0.62, size = 20, normalized size = 0.87 $$\begin{array}{c}\frac{7e^{-x}\log (-\frac{10}{x})\log (x+e^{2x})}{3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-7*x*exp(x)**2-7*x**2)*ln(-10/x)-7*exp(x)**2-7*x)*ln(exp(x)**2+x)+(14*x*exp(x)**2+7*x)*ln(-10/x))
/(3*x*exp(x)**3+3*exp(x)*x**2),x)

[Out]

7*exp(-x)*log(-10/x)*log(x + exp(2*x))/3

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