3.41.11 $\int \frac{76-3x}{-25+x}dx$

Optimal. Leaf size=10 $$-3x+\log (25-x)$$

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.091, Rules used = {43} $$\begin{array}{c}\log (25-x)-3x\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(76 - 3*x)/(-25 + x),x]

[Out]

-3*x + Log[25 - 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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (-3+\frac{1}{-25+x})dx\\ & =-3x+\log (25-x)\end{array}\end{array}$$

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 $$\begin{array}{c}-3(-25+x)+\log (-25+x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(76 - 3*x)/(-25 + x),x]

[Out]

-3*(-25 + x) + Log[-25 + x]

________________________________________________________________________________________

fricas [A]  time = 0.66, size = 8, normalized size = 0.80 $$\begin{array}{c}-3x+\log (x-25)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + log(x - 25)

________________________________________________________________________________________

giac [A]  time = 0.16, size = 9, normalized size = 0.90 $$\begin{array}{c}-3x+\log \left(|x-25|\right)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + log(abs(x - 25))

________________________________________________________________________________________

maple [A]  time = 0.21, size = 9, normalized size = 0.90

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x+ln(x-25)

________________________________________________________________________________________

maxima [A]  time = 0.36, size = 8, normalized size = 0.80 $$\begin{array}{c}-3x+\log (x-25)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + log(x - 25)

________________________________________________________________________________________

mupad [B]  time = 3.78, size = 8, normalized size = 0.80 $$\begin{array}{c}\ln (x-25)-3x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*x - 76)/(x - 25),x)

[Out]

log(x - 25) - 3*x

________________________________________________________________________________________

sympy [A]  time = 0.06, size = 7, normalized size = 0.70 $$\begin{array}{c}-3x+\log (x-25)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + log(x - 25)

________________________________________________________________________________________