3.41.11 \(\int \frac {76-3 x}{-25+x} \, dx\)

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

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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 {gather*} \log (25-x)-3 x \end {gather*}

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 {gather*} \begin {aligned} \text {integral} &=\int \left (-3+\frac {1}{-25+x}\right ) \, dx\\ &=-3 x+\log (25-x)\\ \end {aligned} \end {gather*}

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

Antiderivative was successfully verified.

[In]

Integrate[(76 - 3*x)/(-25 + x),x]

[Out]

-3*(-25 + x) + Log[-25 + x]

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fricas [A]  time = 0.66, size = 8, normalized size = 0.80 \begin {gather*} -3 \, x + \log \left (x - 25\right ) \end {gather*}

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)

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

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))

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

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

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)

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maxima [A]  time = 0.36, size = 8, normalized size = 0.80 \begin {gather*} -3 \, x + \log \left (x - 25\right ) \end {gather*}

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)

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mupad [B]  time = 3.78, size = 8, normalized size = 0.80 \begin {gather*} \ln \left (x-25\right )-3\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*x - 76)/(x - 25),x)

[Out]

log(x - 25) - 3*x

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sympy [A]  time = 0.06, size = 7, normalized size = 0.70 \begin {gather*} - 3 x + \log {\left (x - 25 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + log(x - 25)

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