3.41.45 $\int \frac{-1+\log (x)}{x^2}dx$

Optimal. Leaf size=20 $$\frac{\frac{1}{3}x(1+2\log (3))-\log (x)}{x}$$

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Rubi [A]  time = 0.01, antiderivative size = 7, normalized size of antiderivative = 0.35, number of steps used = 1, number of rules used = 1, integrand size = 8, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.125, Rules used = {2303} $$\begin{array}{c}-\frac{\log (x)}{x}\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =-\frac{\log (x)}{x}\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.35 $$\begin{array}{c}-\frac{\log (x)}{x}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-1 + Log[x])/x^2,x]

[Out]

-(Log[x]/x)

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fricas [A]  time = 0.63, size = 7, normalized size = 0.35 $$\begin{array}{c}-\frac{\log (x)}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-log(x)/x

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giac [A]  time = 0.13, size = 7, normalized size = 0.35 $$\begin{array}{c}-\frac{\log (x)}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-log(x)/x

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maple [A]  time = 0.01, size = 8, normalized size = 0.40

method	result	size
default	$-\frac{\ln (x)}{x}$	$8$
norman	$-\frac{\ln (x)}{x}$	$8$
risch	$-\frac{\ln (x)}{x}$	$8$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(x)-1)/x^2,x,method=_RETURNVERBOSE)

[Out]

-ln(x)/x

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maxima [A]  time = 0.36, size = 13, normalized size = 0.65 $$\begin{array}{c}-\frac{\log (x)+1}{x}+\frac{1}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(log(x) + 1)/x + 1/x

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mupad [B]  time = 2.96, size = 7, normalized size = 0.35 $$\begin{array}{c}-\frac{\ln (x)}{x}\end{array}$$

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 = 0.08, size = 5, normalized size = 0.25 $$\begin{array}{c}-\frac{\log (x)}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-log(x)/x

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