3.87.36 \(\int -\frac {1}{-34+x} \, dx\)

Optimal. Leaf size=8 \[ -\log (34-x) \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {31} \begin {gather*} -\log (34-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-(-34 + x)^(-1),x]

[Out]

-Log[34 - 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 (34-x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} -\log (34-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-(-34 + x)^(-1),x]

[Out]

-Log[34 - x]

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fricas [A]  time = 0.93, size = 6, normalized size = 0.75 \begin {gather*} -\log \left (x - 34\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(x-34),x, algorithm="fricas")

[Out]

-log(x - 34)

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giac [A]  time = 0.22, size = 7, normalized size = 0.88 \begin {gather*} -\log \left ({\left | x - 34 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(x-34),x, algorithm="giac")

[Out]

-log(abs(x - 34))

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maple [A]  time = 0.41, size = 7, normalized size = 0.88

method	result	size
default	\(-\ln \left (x -34\right )\)	\(7\)
norman	\(-\ln \left (x -34\right )\)	\(7\)
risch	\(-\ln \left (x -34\right )\)	\(7\)
meijerg	\(-\ln \left (1-\frac {x}{34}\right )\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(x-34),x,method=_RETURNVERBOSE)

[Out]

-ln(x-34)

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maxima [A]  time = 0.38, size = 6, normalized size = 0.75 \begin {gather*} -\log \left (x - 34\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(x-34),x, algorithm="maxima")

[Out]

-log(x - 34)

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mupad [B]  time = 0.03, size = 6, normalized size = 0.75 \begin {gather*} -\ln \left (x-34\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(x - 34),x)

[Out]

-log(x - 34)

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sympy [A]  time = 0.05, size = 5, normalized size = 0.62 \begin {gather*} - \log {\left (x - 34 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(x-34),x)

[Out]

-log(x - 34)

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