3.55.90 \(\int \frac {1-4 x}{x} \, dx\)

Optimal. Leaf size=15 \[ x \left (-3+\frac {-5-x+\log (x)}{x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.40, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {43} \begin {gather*} \log (x)-4 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 4*x)/x,x]

[Out]

-4*x + Log[x]

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-4+\frac {1}{x}\right ) \, dx\\ &=-4 x+\log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 6, normalized size = 0.40 \begin {gather*} -4 x+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 4*x)/x,x]

[Out]

-4*x + Log[x]

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fricas [A]  time = 0.66, size = 6, normalized size = 0.40 \begin {gather*} -4 \, x + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+1)/x,x, algorithm="fricas")

[Out]

-4*x + log(x)

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giac [A]  time = 1.01, size = 7, normalized size = 0.47 \begin {gather*} -4 \, x + \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+1)/x,x, algorithm="giac")

[Out]

-4*x + log(abs(x))

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maple [A]  time = 0.02, size = 7, normalized size = 0.47

method	result	size
default	\(-4 x +\ln \relax (x )\)	\(7\)
norman	\(-4 x +\ln \relax (x )\)	\(7\)
risch	\(-4 x +\ln \relax (x )\)	\(7\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*x+1)/x,x,method=_RETURNVERBOSE)

[Out]

-4*x+ln(x)

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maxima [A]  time = 0.38, size = 6, normalized size = 0.40 \begin {gather*} -4 \, x + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+1)/x,x, algorithm="maxima")

[Out]

-4*x + log(x)

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mupad [B]  time = 0.01, size = 6, normalized size = 0.40 \begin {gather*} \ln \relax (x)-4\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*x - 1)/x,x)

[Out]

log(x) - 4*x

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sympy [A]  time = 0.06, size = 5, normalized size = 0.33 \begin {gather*} - 4 x + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+1)/x,x)

[Out]

-4*x + log(x)

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