3.89.55 \(\int \frac {-2 x-2 \log ^4(2)}{\log ^4(2)} \, dx\)

Optimal. Leaf size=13 \[ -2 x-\frac {x^2}{\log ^4(2)} \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.08, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {9} \begin {gather*} -\frac {\left (x+\log ^4(2)\right )^2}{\log ^4(2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2*x - 2*Log[2]^4)/Log[2]^4,x]

[Out]

-((x + Log[2]^4)^2/Log[2]^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} &=-\frac {\left (x+\log ^4(2)\right )^2}{\log ^4(2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} -2 x-\frac {x^2}{\log ^4(2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x - 2*Log[2]^4)/Log[2]^4,x]

[Out]

-2*x - x^2/Log[2]^4

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fricas [A]  time = 0.59, size = 17, normalized size = 1.31 \begin {gather*} -\frac {2 \, x \log \relax (2)^{4} + x^{2}}{\log \relax (2)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*log(2)^4-2*x)/log(2)^4,x, algorithm="fricas")

[Out]

-(2*x*log(2)^4 + x^2)/log(2)^4

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giac [A]  time = 0.14, size = 17, normalized size = 1.31 \begin {gather*} -\frac {2 \, x \log \relax (2)^{4} + x^{2}}{\log \relax (2)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*log(2)^4-2*x)/log(2)^4,x, algorithm="giac")

[Out]

-(2*x*log(2)^4 + x^2)/log(2)^4

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maple [A]  time = 0.03, size = 14, normalized size = 1.08

method	result	size
risch	\(-\frac {x^{2}}{\ln \relax (2)^{4}}-2 x\)	\(14\)
gosper	\(-\frac {x \left (2 \ln \relax (2)^{4}+x \right )}{\ln \relax (2)^{4}}\)	\(16\)
default	\(\frac {-2 x \ln \relax (2)^{4}-x^{2}}{\ln \relax (2)^{4}}\)	\(19\)
norman	\(\frac {-2 x \ln \relax (2)^{3}-\frac {x^{2}}{\ln \relax (2)}}{\ln \relax (2)^{3}}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2*ln(2)^4-2*x)/ln(2)^4,x,method=_RETURNVERBOSE)

[Out]

-x^2/ln(2)^4-2*x

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maxima [A]  time = 0.37, size = 17, normalized size = 1.31 \begin {gather*} -\frac {2 \, x \log \relax (2)^{4} + x^{2}}{\log \relax (2)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*log(2)^4-2*x)/log(2)^4,x, algorithm="maxima")

[Out]

-(2*x*log(2)^4 + x^2)/log(2)^4

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mupad [B]  time = 0.08, size = 14, normalized size = 1.08 \begin {gather*} -\frac {{\left (x+{\ln \relax (2)}^4\right )}^2}{{\ln \relax (2)}^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x + 2*log(2)^4)/log(2)^4,x)

[Out]

-(x + log(2)^4)^2/log(2)^4

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sympy [A]  time = 0.05, size = 12, normalized size = 0.92 \begin {gather*} - \frac {x^{2}}{\log {\relax (2 )}^{4}} - 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*ln(2)**4-2*x)/ln(2)**4,x)

[Out]

-x**2/log(2)**4 - 2*x

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