\(\int -\frac {1}{-34+x} \, dx\) [8636]

Optimal result

Integrand size = 7, antiderivative size = 8 \[ \int -\frac {1}{-34+x} \, dx=-\log (34-x) \]

[Out]

-ln(34-x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {31} \[ \int -\frac {1}{-34+x} \, dx=-\log (34-x) \]

[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{align*} \text {integral}& = -\log (34-x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int -\frac {1}{-34+x} \, dx=-\log (34-x) \]

[In]

Integrate[-(-34 + x)^(-1),x]

[Out]

-Log[34 - x]

Maple [A] (verified)

Time = 0.53 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88

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

[In]

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

[Out]

-ln(x-34)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int -\frac {1}{-34+x} \, dx=-\log \left (x - 34\right ) \]

[In]

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

[Out]

-log(x - 34)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int -\frac {1}{-34+x} \, dx=- \log {\left (x - 34 \right )} \]

[In]

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

[Out]

-log(x - 34)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int -\frac {1}{-34+x} \, dx=-\log \left (x - 34\right ) \]

[In]

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

[Out]

-log(x - 34)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int -\frac {1}{-34+x} \, dx=-\log \left ({\left | x - 34 \right |}\right ) \]

[In]

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

[Out]

-log(abs(x - 34))

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int -\frac {1}{-34+x} \, dx=-\ln \left (x-34\right ) \]

[In]

int(-1/(x - 34),x)

[Out]

-log(x - 34)