3.29.17 \(\int (-6-2 x) \log (4) \, dx\) [2817]

Optimal. Leaf size=16 \[ -4+x-x (1+(6+x) \log (4))+\log (5) \]

[Out]

ln(5)-4+x-(2*ln(2)*(6+x)+1)*x

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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.56, number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {9} \begin {gather*} -(x+3)^2 \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-6 - 2*x)*Log[4],x]

[Out]

-((3 + x)^2*Log[4])

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[a*((b + c*x)^2/(2*c)), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-(3+x)^2 \log (4)\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} -2 \left (3 x+\frac {x^2}{2}\right ) \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6 - 2*x)*Log[4],x]

[Out]

-2*(3*x + x^2/2)*Log[4]

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Maple [A]
time = 0.16, size = 14, normalized size = 0.88

method	result	size
gosper	\(-2 \ln \left (2\right ) \left (x +6\right ) x\)	\(9\)
default	\(2 \left (-x^{2}-6 x \right ) \ln \left (2\right )\)	\(14\)
norman	\(-12 x \ln \left (2\right )-2 x^{2} \ln \left (2\right )\)	\(14\)
risch	\(-12 x \ln \left (2\right )-2 x^{2} \ln \left (2\right )\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*(-2*x-6)*ln(2),x,method=_RETURNVERBOSE)

[Out]

2*(-x^2-6*x)*ln(2)

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Maxima [A]
time = 0.27, size = 11, normalized size = 0.69 \begin {gather*} -2 \, {\left (x^{2} + 6 \, x\right )} \log \left (2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-2*x-6)*log(2),x, algorithm="maxima")

[Out]

-2*(x^2 + 6*x)*log(2)

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Fricas [A]
time = 0.38, size = 11, normalized size = 0.69 \begin {gather*} -2 \, {\left (x^{2} + 6 \, x\right )} \log \left (2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-2*x-6)*log(2),x, algorithm="fricas")

[Out]

-2*(x^2 + 6*x)*log(2)

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Sympy [A]
time = 0.01, size = 15, normalized size = 0.94 \begin {gather*} - 2 x^{2} \log {\left (2 \right )} - 12 x \log {\left (2 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-2*x-6)*ln(2),x)

[Out]

-2*x**2*log(2) - 12*x*log(2)

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Giac [A]
time = 0.39, size = 11, normalized size = 0.69 \begin {gather*} -2 \, {\left (x^{2} + 6 \, x\right )} \log \left (2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-2*x-6)*log(2),x, algorithm="giac")

[Out]

-2*(x^2 + 6*x)*log(2)

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Mupad [B]
time = 1.70, size = 9, normalized size = 0.56 \begin {gather*} -2\,\ln \left (2\right )\,{\left (x+3\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*log(2)*(2*x + 6),x)

[Out]

-2*log(2)*(x + 3)^2

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