### 3.288 $$\int \frac{1}{x+\log (x)} \, dx$$

Optimal. Leaf size=8 $\text{CannotIntegrate}\left (\frac{1}{x+\log (x)},x\right )$

[Out]

CannotIntegrate[(x + Log[x])^(-1), x]

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Rubi [A]  time = 0.0078645, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., Rules used = {} $\int \frac{1}{x+\log (x)} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[(x + Log[x])^(-1),x]

[Out]

Defer[Int][(x + Log[x])^(-1), x]

Rubi steps

\begin{align*} \int \frac{1}{x+\log (x)} \, dx &=\int \frac{1}{x+\log (x)} \, dx\\ \end{align*}

Mathematica [A]  time = 0.005806, size = 0, normalized size = 0. $\int \frac{1}{x+\log (x)} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[(x + Log[x])^(-1),x]

[Out]

Integrate[(x + Log[x])^(-1), x]

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Maple [A]  time = 0.009, size = 0, normalized size = 0. \begin{align*} \int \left ( x+\ln \left ( x \right ) \right ) ^{-1}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x+ln(x)),x)

[Out]

int(1/(x+ln(x)),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x + \log \left (x\right )}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(x+log(x)),x, algorithm="maxima")

[Out]

integrate(1/(x + log(x)), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x + \log \left (x\right )}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(x+log(x)),x, algorithm="fricas")

[Out]

integral(1/(x + log(x)), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x + \log{\left (x \right )}}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(x+ln(x)),x)

[Out]

Integral(1/(x + log(x)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x + \log \left (x\right )}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(x+log(x)),x, algorithm="giac")

[Out]

integrate(1/(x + log(x)), x)