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

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

[Out]

ln(x)/x

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Rubi [A]  time = 0.01, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, 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*}

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Mathematica [A]  time = 0.00, size = 6, normalized size = 1.00 \[ \frac {\log (x)}{x} \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - Log[x])/x^2,x]

[Out]

Log[x]/x

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fricas [A]  time = 0.43, size = 6, normalized size = 1.00 \[ \frac {\log \relax (x)}{x} \]

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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giac [A]  time = 0.16, size = 6, normalized size = 1.00 \[ \frac {\log \relax (x)}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

log(x)/x

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maple [A]  time = 0.06, size = 7, normalized size = 1.17 \[ \frac {\ln \relax (x )}{x} \]

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 = 0.76, size = 14, normalized size = 2.33 \[ \frac {\log \relax (x) + 1}{x} - \frac {1}{x} \]

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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mupad [B]  time = 0.35, size = 6, normalized size = 1.00 \[ \frac {\ln \relax (x)}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x) - 1)/x^2,x)

[Out]

log(x)/x

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sympy [A]  time = 0.09, size = 3, normalized size = 0.50 \[ \frac {\log {\relax (x )}}{x} \]

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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