\(\int \frac {14}{-3+4 x} \, dx\) [7596]

Optimal result

Integrand size = 9, antiderivative size = 20 \[ \int \frac {14}{-3+4 x} \, dx=7 \left (5-\log (5)+\frac {1}{2} (-1+\log (-3+4 x))\right ) \]

[Out]

63/2-7*ln(5)+7/2*ln(-3+4*x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.50, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 31} \[ \int \frac {14}{-3+4 x} \, dx=\frac {7}{2} \log (3-4 x) \]

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.50 \[ \int \frac {14}{-3+4 x} \, dx=\frac {7}{2} \log (-3+4 x) \]

[In]

Integrate[14/(-3 + 4*x),x]

[Out]

(7*Log[-3 + 4*x])/2

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.35

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

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.40 \[ \int \frac {14}{-3+4 x} \, dx=\frac {7}{2} \, \log \left (4 \, x - 3\right ) \]

[In]

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

[Out]

7/2*log(4*x - 3)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.40 \[ \int \frac {14}{-3+4 x} \, dx=\frac {7 \log {\left (4 x - 3 \right )}}{2} \]

[In]

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

[Out]

7*log(4*x - 3)/2

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.40 \[ \int \frac {14}{-3+4 x} \, dx=\frac {7}{2} \, \log \left (4 \, x - 3\right ) \]

[In]

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

[Out]

7/2*log(4*x - 3)

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int \frac {14}{-3+4 x} \, dx=\frac {7}{2} \, \log \left ({\left | 4 \, x - 3 \right |}\right ) \]

[In]

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

[Out]

7/2*log(abs(4*x - 3))

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.30 \[ \int \frac {14}{-3+4 x} \, dx=\frac {7\,\ln \left (x-\frac {3}{4}\right )}{2} \]

[In]

int(14/(4*x - 3),x)

[Out]

(7*log(x - 3/4))/2