### 3.237 $$\int \frac{1-\log (x)}{x^2} \, dx$$

Optimal. Leaf size=6 $\frac{\log (x)}{x}$

[Out]

Log[x]/x

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Rubi [A]  time = 0.0104505, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0.1, Rules used = {2303} $\frac{\log (x)}{x}$

Antiderivative was successfully veriﬁed.

[In]

Int[(1 - Log[x])/x^2,x]

[Out]

Log[x]/x

Rule 2303

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(b*(d*x)^(m + 1)*Log[c*x^n])/(
d*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1] && EqQ[a*(m + 1) - b*n, 0]

Rubi steps

\begin{align*} \int \frac{1-\log (x)}{x^2} \, dx &=\frac{\log (x)}{x}\\ \end{align*}

Mathematica [A]  time = 0.0012218, size = 6, normalized size = 1. $\frac{\log (x)}{x}$

Antiderivative was successfully veriﬁed.

[In]

Integrate[(1 - Log[x])/x^2,x]

[Out]

Log[x]/x

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Maple [A]  time = 0.001, size = 7, normalized size = 1.2 \begin{align*}{\frac{\ln \left ( x \right ) }{x}} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((1-ln(x))/x^2,x)

[Out]

ln(x)/x

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Maxima [B]  time = 1.09091, size = 19, normalized size = 3.17 \begin{align*} \frac{\log \left (x\right ) + 1}{x} - \frac{1}{x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-log(x))/x^2,x, algorithm="maxima")

[Out]

(log(x) + 1)/x - 1/x

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Fricas [A]  time = 1.71323, size = 14, normalized size = 2.33 \begin{align*} \frac{\log \left (x\right )}{x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-log(x))/x^2,x, algorithm="fricas")

[Out]

log(x)/x

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Sympy [A]  time = 0.090357, size = 3, normalized size = 0.5 \begin{align*} \frac{\log{\left (x \right )}}{x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-ln(x))/x**2,x)

[Out]

log(x)/x

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Giac [A]  time = 1.31882, size = 8, normalized size = 1.33 \begin{align*} \frac{\log \left (x\right )}{x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-log(x))/x^2,x, algorithm="giac")

[Out]

log(x)/x