\(\int \frac {59-10 x}{-6+x} \, dx\) [9655]

Optimal result

Integrand size = 11, antiderivative size = 12 \[ \int \frac {59-10 x}{-6+x} \, dx=-10 x-\log (6-x) \]

[Out]

-10*x-ln(6-x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45} \[ \int \frac {59-10 x}{-6+x} \, dx=-10 x-\log (6-x) \]

[In]

Int[(59 - 10*x)/(-6 + x),x]

[Out]

-10*x - Log[6 - x]

Rule 45

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{align*} \text {integral}& = \int \left (-10+\frac {1}{6-x}\right ) \, dx \\ & = -10 x-\log (6-x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {59-10 x}{-6+x} \, dx=-10 (-6+x)-\log (-6+x) \]

[In]

Integrate[(59 - 10*x)/(-6 + x),x]

[Out]

-10*(-6 + x) - Log[-6 + x]

Maple [A] (verified)

Time = 0.70 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92

method	result	size
default	\(-10 x -\ln \left (-6+x \right )\)	\(11\)
norman	\(-10 x -\ln \left (-6+x \right )\)	\(11\)
risch	\(-10 x -\ln \left (-6+x \right )\)	\(11\)
parallelrisch	\(-10 x -\ln \left (-6+x \right )\)	\(11\)
meijerg	\(-\ln \left (1-\frac {x}{6}\right )-10 x\)	\(13\)

[In]

int((-10*x+59)/(-6+x),x,method=_RETURNVERBOSE)

[Out]

-10*x-ln(-6+x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {59-10 x}{-6+x} \, dx=-10 \, x - \log \left (x - 6\right ) \]

[In]

integrate((-10*x+59)/(-6+x),x, algorithm="fricas")

[Out]

-10*x - log(x - 6)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {59-10 x}{-6+x} \, dx=- 10 x - \log {\left (x - 6 \right )} \]

[In]

integrate((-10*x+59)/(-6+x),x)

[Out]

-10*x - log(x - 6)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {59-10 x}{-6+x} \, dx=-10 \, x - \log \left (x - 6\right ) \]

[In]

integrate((-10*x+59)/(-6+x),x, algorithm="maxima")

[Out]

-10*x - log(x - 6)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \frac {59-10 x}{-6+x} \, dx=-10 \, x - \log \left ({\left | x - 6 \right |}\right ) \]

[In]

integrate((-10*x+59)/(-6+x),x, algorithm="giac")

[Out]

-10*x - log(abs(x - 6))

Mupad [B] (verification not implemented)

Time = 13.90 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {59-10 x}{-6+x} \, dx=-10\,x-\ln \left (x-6\right ) \]

[In]

int(-(10*x - 59)/(x - 6),x)

[Out]

- 10*x - log(x - 6)