3.47.36 \(\int (2+(-2 x+8 x^3) \log (2)) \, dx\) [4636]

Optimal. Leaf size=19 \[ -x^2 \log (2)+2 x \left (1+x^3 \log (2)\right ) \]

[Out]

2*(x^3*ln(2)+1)*x-x^2*ln(2)

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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 0, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 2 x^4 \log (2)-x^2 \log (2)+2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2 + (-2*x + 8*x^3)*Log[2],x]

[Out]

2*x - x^2*Log[2] + 2*x^4*Log[2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 x+\log (2) \int \left (-2 x+8 x^3\right ) \, dx\\ &=2 x-x^2 \log (2)+2 x^4 \log (2)\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 20, normalized size = 1.05 \begin {gather*} 2 x+2 x^4 \log (2)-\frac {1}{2} x^2 \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2 + (-2*x + 8*x^3)*Log[2],x]

[Out]

2*x + 2*x^4*Log[2] - (x^2*Log[4])/2

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Maple [A]
time = 0.27, size = 19, normalized size = 1.00

method	result	size
gosper	\(x \left (2 x^{3} \ln \left (2\right )-x \ln \left (2\right )+2\right )\)	\(17\)
default	\(2 x^{4} \ln \left (2\right )-x^{2} \ln \left (2\right )+2 x\)	\(19\)
norman	\(2 x^{4} \ln \left (2\right )-x^{2} \ln \left (2\right )+2 x\)	\(19\)
risch	\(2 x^{4} \ln \left (2\right )-x^{2} \ln \left (2\right )+\frac {\ln \left (2\right )}{8}+2 x\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*x^3-2*x)*ln(2)+2,x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.29, size = 18, normalized size = 0.95 \begin {gather*} {\left (2 \, x^{4} - x^{2}\right )} \log \left (2\right ) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^3-2*x)*log(2)+2,x, algorithm="maxima")

[Out]

(2*x^4 - x^2)*log(2) + 2*x

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Fricas [A]
time = 0.33, size = 18, normalized size = 0.95 \begin {gather*} {\left (2 \, x^{4} - x^{2}\right )} \log \left (2\right ) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^3-2*x)*log(2)+2,x, algorithm="fricas")

[Out]

(2*x^4 - x^2)*log(2) + 2*x

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Sympy [A]
time = 0.01, size = 17, normalized size = 0.89 \begin {gather*} 2 x^{4} \log {\left (2 \right )} - x^{2} \log {\left (2 \right )} + 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x**3-2*x)*ln(2)+2,x)

[Out]

2*x**4*log(2) - x**2*log(2) + 2*x

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Giac [A]
time = 0.42, size = 18, normalized size = 0.95 \begin {gather*} {\left (2 \, x^{4} - x^{2}\right )} \log \left (2\right ) + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^3-2*x)*log(2)+2,x, algorithm="giac")

[Out]

(2*x^4 - x^2)*log(2) + 2*x

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Mupad [B]
time = 0.04, size = 16, normalized size = 0.84 \begin {gather*} x\,\left (2\,\ln \left (2\right )\,x^3-\ln \left (2\right )\,x+2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2 - log(2)*(2*x - 8*x^3),x)

[Out]

x*(2*x^3*log(2) - x*log(2) + 2)

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