3.76.96 \(\int \frac {14}{-3+4 x} \, dx\)

Optimal. Leaf size=20 \[ 7 \left (5-\log (5)+\frac {1}{2} (-1+\log (-3+4 x))\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.50, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 31} \begin {gather*} \frac {7}{2} \log (3-4 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[14/(-3 + 4*x),x]

[Out]

(7*Log[3 - 4*x])/2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=14 \int \frac {1}{-3+4 x} \, dx\\ &=\frac {7}{2} \log (3-4 x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.50 \begin {gather*} \frac {7}{2} \log (-3+4 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[14/(-3 + 4*x),x]

[Out]

(7*Log[-3 + 4*x])/2

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fricas [A]  time = 0.67, size = 8, normalized size = 0.40 \begin {gather*} \frac {7}{2} \, \log \left (4 \, x - 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14/(4*x-3),x, algorithm="fricas")

[Out]

7/2*log(4*x - 3)

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giac [A]  time = 0.24, size = 9, normalized size = 0.45 \begin {gather*} \frac {7}{2} \, \log \left ({\left | 4 \, x - 3 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14/(4*x-3),x, algorithm="giac")

[Out]

7/2*log(abs(4*x - 3))

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maple [A]  time = 0.21, size = 9, normalized size = 0.45

method	result	size
default	\(\frac {7 \ln \left (4 x -3\right )}{2}\)	\(9\)
norman	\(\frac {7 \ln \left (4 x -3\right )}{2}\)	\(9\)
meijerg	\(\frac {7 \ln \left (1-\frac {4 x}{3}\right )}{2}\)	\(9\)
risch	\(\frac {7 \ln \left (4 x -3\right )}{2}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(14/(4*x-3),x,method=_RETURNVERBOSE)

[Out]

7/2*ln(4*x-3)

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maxima [A]  time = 0.36, size = 8, normalized size = 0.40 \begin {gather*} \frac {7}{2} \, \log \left (4 \, x - 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14/(4*x-3),x, algorithm="maxima")

[Out]

7/2*log(4*x - 3)

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mupad [B]  time = 0.06, size = 6, normalized size = 0.30 \begin {gather*} \frac {7\,\ln \left (x-\frac {3}{4}\right )}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(14/(4*x - 3),x)

[Out]

(7*log(x - 3/4))/2

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sympy [A]  time = 0.06, size = 8, normalized size = 0.40 \begin {gather*} \frac {7 \log {\left (4 x - 3 \right )}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14/(4*x-3),x)

[Out]

7*log(4*x - 3)/2

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