3.29.100 \(\int \frac {-17+24 x}{12 x} \, dx\)

Optimal. Leaf size=10 \[ 2 x-\frac {17 \log (x)}{12} \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 43} \begin {gather*} 2 x-\frac {17 \log (x)}{12} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-17 + 24*x)/(12*x),x]

[Out]

2*x - (17*Log[x])/12

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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} &=\frac {1}{12} \int \frac {-17+24 x}{x} \, dx\\ &=\frac {1}{12} \int \left (24-\frac {17}{x}\right ) \, dx\\ &=2 x-\frac {17 \log (x)}{12}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} 2 x-\frac {17 \log (x)}{12} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-17 + 24*x)/(12*x),x]

[Out]

2*x - (17*Log[x])/12

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fricas [A]  time = 0.58, size = 8, normalized size = 0.80 \begin {gather*} 2 \, x - \frac {17}{12} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/12*(24*x-17)/x,x, algorithm="fricas")

[Out]

2*x - 17/12*log(x)

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giac [A]  time = 0.21, size = 9, normalized size = 0.90 \begin {gather*} 2 \, x - \frac {17}{12} \, \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/12*(24*x-17)/x,x, algorithm="giac")

[Out]

2*x - 17/12*log(abs(x))

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maple [A]  time = 0.02, size = 9, normalized size = 0.90

method	result	size
default	\(2 x -\frac {17 \ln \relax (x )}{12}\)	\(9\)
norman	\(2 x -\frac {17 \ln \relax (x )}{12}\)	\(9\)
risch	\(2 x -\frac {17 \ln \relax (x )}{12}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/12*(24*x-17)/x,x,method=_RETURNVERBOSE)

[Out]

2*x-17/12*ln(x)

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maxima [A]  time = 0.62, size = 8, normalized size = 0.80 \begin {gather*} 2 \, x - \frac {17}{12} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/12*(24*x-17)/x,x, algorithm="maxima")

[Out]

2*x - 17/12*log(x)

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mupad [B]  time = 0.02, size = 8, normalized size = 0.80 \begin {gather*} 2\,x-\frac {17\,\ln \relax (x)}{12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x - 17/12)/x,x)

[Out]

2*x - (17*log(x))/12

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sympy [A]  time = 0.06, size = 8, normalized size = 0.80 \begin {gather*} 2 x - \frac {17 \log {\relax (x )}}{12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/12*(24*x-17)/x,x)

[Out]

2*x - 17*log(x)/12

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