3.3.96 \(\int \frac {1}{-10+x} \, dx\)

Optimal. Leaf size=17 \[ \log \left (\frac {5+\frac {1}{2} (10-2 x)}{\log (2)}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.35, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {31} \begin {gather*} \log (10-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-10 + x)^(-1),x]

[Out]

Log[10 - x]

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log (10-x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 4, normalized size = 0.24 \begin {gather*} \log (-10+x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-10 + x)^(-1),x]

[Out]

Log[-10 + x]

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fricas [A]  time = 0.65, size = 4, normalized size = 0.24 \begin {gather*} \log \left (x - 10\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(x-10),x, algorithm="fricas")

[Out]

log(x - 10)

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giac [A]  time = 0.35, size = 5, normalized size = 0.29 \begin {gather*} \log \left ({\left | x - 10 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(x-10),x, algorithm="giac")

[Out]

log(abs(x - 10))

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maple [A]  time = 0.20, size = 5, normalized size = 0.29

method	result	size
default	\(\ln \left (x -10\right )\)	\(5\)
norman	\(\ln \left (x -10\right )\)	\(5\)
risch	\(\ln \left (x -10\right )\)	\(5\)
meijerg	\(\ln \left (1-\frac {x}{10}\right )\)	\(7\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x-10),x,method=_RETURNVERBOSE)

[Out]

ln(x-10)

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maxima [A]  time = 0.52, size = 4, normalized size = 0.24 \begin {gather*} \log \left (x - 10\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(x-10),x, algorithm="maxima")

[Out]

log(x - 10)

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mupad [B]  time = 0.02, size = 4, normalized size = 0.24 \begin {gather*} \ln \left (x-10\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x - 10),x)

[Out]

log(x - 10)

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sympy [A]  time = 0.06, size = 3, normalized size = 0.18 \begin {gather*} \log {\left (x - 10 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(x-10),x)

[Out]

log(x - 10)

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