\(\int \frac {76-3 x}{-25+x} \, dx\) [4011]

Optimal result

Integrand size = 11, antiderivative size = 10 \[ \int \frac {76-3 x}{-25+x} \, dx=-3 x+\log (25-x) \]

[Out]

ln(-x+25)-3*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, 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} \[ \int \frac {76-3 x}{-25+x} \, dx=\log (25-x)-3 x \]

[In]

Int[(76 - 3*x)/(-25 + x),x]

[Out]

-3*x + Log[25 - 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 (-3+\frac {1}{-25+x}\right ) \, dx \\ & = -3 x+\log (25-x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {76-3 x}{-25+x} \, dx=-3 (-25+x)+\log (-25+x) \]

[In]

Integrate[(76 - 3*x)/(-25 + x),x]

[Out]

-3*(-25 + x) + Log[-25 + x]

Maple [A] (verified)

Time = 1.62 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90

method	result	size
default	\(-3 x +\ln \left (x -25\right )\)	\(9\)
norman	\(-3 x +\ln \left (x -25\right )\)	\(9\)
risch	\(-3 x +\ln \left (x -25\right )\)	\(9\)
parallelrisch	\(-3 x +\ln \left (x -25\right )\)	\(9\)
meijerg	\(\ln \left (1-\frac {x}{25}\right )-3 x\)	\(11\)

[In]

int((-3*x+76)/(x-25),x,method=_RETURNVERBOSE)

[Out]

-3*x+ln(x-25)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {76-3 x}{-25+x} \, dx=-3 \, x + \log \left (x - 25\right ) \]

[In]

integrate((-3*x+76)/(x-25),x, algorithm="fricas")

[Out]

-3*x + log(x - 25)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \frac {76-3 x}{-25+x} \, dx=- 3 x + \log {\left (x - 25 \right )} \]

[In]

integrate((-3*x+76)/(x-25),x)

[Out]

-3*x + log(x - 25)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {76-3 x}{-25+x} \, dx=-3 \, x + \log \left (x - 25\right ) \]

[In]

integrate((-3*x+76)/(x-25),x, algorithm="maxima")

[Out]

-3*x + log(x - 25)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int \frac {76-3 x}{-25+x} \, dx=-3 \, x + \log \left ({\left | x - 25 \right |}\right ) \]

[In]

integrate((-3*x+76)/(x-25),x, algorithm="giac")

[Out]

-3*x + log(abs(x - 25))

Mupad [B] (verification not implemented)

Time = 10.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {76-3 x}{-25+x} \, dx=\ln \left (x-25\right )-3\,x \]

[In]

int(-(3*x - 76)/(x - 25),x)

[Out]

log(x - 25) - 3*x