3.86.6 \(\int \frac {-4+8 x \log (2)}{\log (2)} \, dx\)

Optimal. Leaf size=24 \[ 4 \left (-\frac {1}{9}+x^2+\frac {x-x^2}{x \log (2)}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.58, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {9} \begin {gather*} \frac {(1-2 x \log (2))^2}{\log ^2(2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-4 + 8*x*Log[2])/Log[2],x]

[Out]

(1 - 2*x*Log[2])^2/Log[2]^2

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 {(1-2 x \log (2))^2}{\log ^2(2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.54 \begin {gather*} 4 x^2-\frac {4 x}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4 + 8*x*Log[2])/Log[2],x]

[Out]

4*x^2 - (4*x)/Log[2]

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fricas [A]  time = 0.96, size = 16, normalized size = 0.67 \begin {gather*} \frac {4 \, {\left (x^{2} \log \relax (2) - x\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x*log(2)-4)/log(2),x, algorithm="fricas")

[Out]

4*(x^2*log(2) - x)/log(2)

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giac [A]  time = 0.20, size = 16, normalized size = 0.67 \begin {gather*} \frac {4 \, {\left (x^{2} \log \relax (2) - x\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x*log(2)-4)/log(2),x, algorithm="giac")

[Out]

4*(x^2*log(2) - x)/log(2)

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maple [A]  time = 0.02, size = 14, normalized size = 0.58

method	result	size
gosper	\(\frac {4 x \left (x \ln \relax (2)-1\right )}{\ln \relax (2)}\)	\(14\)
norman	\(4 x^{2}-\frac {4 x}{\ln \relax (2)}\)	\(14\)
risch	\(4 x^{2}-\frac {4 x}{\ln \relax (2)}\)	\(14\)
default	\(\frac {4 x^{2} \ln \relax (2)-4 x}{\ln \relax (2)}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*x*ln(2)-4)/ln(2),x,method=_RETURNVERBOSE)

[Out]

4*x*(x*ln(2)-1)/ln(2)

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maxima [A]  time = 0.35, size = 16, normalized size = 0.67 \begin {gather*} \frac {4 \, {\left (x^{2} \log \relax (2) - x\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x*log(2)-4)/log(2),x, algorithm="maxima")

[Out]

4*(x^2*log(2) - x)/log(2)

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mupad [B]  time = 0.08, size = 15, normalized size = 0.62 \begin {gather*} \frac {{\left (8\,x\,\ln \relax (2)-4\right )}^2}{16\,{\ln \relax (2)}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*x*log(2) - 4)/log(2),x)

[Out]

(8*x*log(2) - 4)^2/(16*log(2)^2)

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sympy [A]  time = 0.05, size = 10, normalized size = 0.42 \begin {gather*} 4 x^{2} - \frac {4 x}{\log {\relax (2 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x*ln(2)-4)/ln(2),x)

[Out]

4*x**2 - 4*x/log(2)

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