3.87.56 \(\int -\frac {1}{7+x} \, dx\)

Optimal. Leaf size=10 \[ 8-\log (-7-x) \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.60, 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 (x+7) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-(7 + x)^(-1),x]

[Out]

-Log[7 + 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 (7+x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 6, normalized size = 0.60 \begin {gather*} -\log (7+x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-(7 + x)^(-1),x]

[Out]

-Log[7 + x]

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fricas [A]  time = 0.44, size = 6, normalized size = 0.60 \begin {gather*} -\log \left (x + 7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(x+7),x, algorithm="fricas")

[Out]

-log(x + 7)

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giac [A]  time = 0.18, size = 7, normalized size = 0.70 \begin {gather*} -\log \left ({\left | x + 7 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(x+7),x, algorithm="giac")

[Out]

-log(abs(x + 7))

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maple [A]  time = 0.41, size = 7, normalized size = 0.70

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(x+7),x,method=_RETURNVERBOSE)

[Out]

-ln(x+7)

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maxima [A]  time = 0.37, size = 6, normalized size = 0.60 \begin {gather*} -\log \left (x + 7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(x+7),x, algorithm="maxima")

[Out]

-log(x + 7)

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mupad [B]  time = 0.02, size = 6, normalized size = 0.60 \begin {gather*} -\ln \left (x+7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(x + 7),x)

[Out]

-log(x + 7)

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sympy [A]  time = 0.05, size = 5, normalized size = 0.50 \begin {gather*} - \log {\left (x + 7 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/(x+7),x)

[Out]

-log(x + 7)

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