3.97.55 \(\int \frac {59-10 x}{-6+x} \, dx\)

Optimal. Leaf size=12 \[ -10 x-\log (6-x) \]

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Rubi [A]  time = 0.01, antiderivative size = 12, 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*} -10 x-\log (6-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(59 - 10*x)/(-6 + x),x]

[Out]

-10*x - Log[6 - 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 (-10+\frac {1}{6-x}\right ) \, dx\\ &=-10 x-\log (6-x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -10 (-6+x)-\log (-6+x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(59 - 10*x)/(-6 + x),x]

[Out]

-10*(-6 + x) - Log[-6 + x]

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fricas [A]  time = 0.64, size = 10, normalized size = 0.83 \begin {gather*} -10 \, x - \log \left (x - 6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10*x - log(x - 6)

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giac [A]  time = 0.13, size = 11, normalized size = 0.92 \begin {gather*} -10 \, x - \log \left ({\left | x - 6 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10*x - log(abs(x - 6))

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maple [A]  time = 0.08, size = 11, normalized size = 0.92

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10*x-ln(x-6)

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maxima [A]  time = 0.36, size = 10, normalized size = 0.83 \begin {gather*} -10 \, x - \log \left (x - 6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10*x - log(x - 6)

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mupad [B]  time = 6.96, size = 10, normalized size = 0.83 \begin {gather*} -10\,x-\ln \left (x-6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(10*x - 59)/(x - 6),x)

[Out]

- 10*x - log(x - 6)

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sympy [A]  time = 0.06, size = 8, normalized size = 0.67 \begin {gather*} - 10 x - \log {\left (x - 6 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10*x - log(x - 6)

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