3.45.23 \(\int (-4 x-4 x^3+\log (3)) \, dx\)

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

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^4-2 x^2+x \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-4*x - 4*x^3 + Log[3],x]

[Out]

-2*x^2 - x^4 + x*Log[3]

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 15, normalized size = 0.79 \begin {gather*} -2 x^2-x^4+x \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-4*x - 4*x^3 + Log[3],x]

[Out]

-2*x^2 - x^4 + x*Log[3]

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fricas [A]  time = 0.55, size = 15, normalized size = 0.79 \begin {gather*} -x^{4} - 2 \, x^{2} + x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(3)-4*x^3-4*x,x, algorithm="fricas")

[Out]

-x^4 - 2*x^2 + x*log(3)

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giac [A]  time = 0.21, size = 15, normalized size = 0.79 \begin {gather*} -x^{4} - 2 \, x^{2} + x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(3)-4*x^3-4*x,x, algorithm="giac")

[Out]

-x^4 - 2*x^2 + x*log(3)

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maple [A]  time = 0.02, size = 16, normalized size = 0.84

method	result	size
gosper	\(-x^{4}-2 x^{2}+x \ln \relax (3)\)	\(16\)
default	\(-x^{4}-2 x^{2}+x \ln \relax (3)\)	\(16\)
norman	\(-x^{4}-2 x^{2}+x \ln \relax (3)\)	\(16\)
risch	\(-x^{4}-2 x^{2}+x \ln \relax (3)\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(3)-4*x^3-4*x,x,method=_RETURNVERBOSE)

[Out]

-x^4-2*x^2+x*ln(3)

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maxima [A]  time = 0.37, size = 15, normalized size = 0.79 \begin {gather*} -x^{4} - 2 \, x^{2} + x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(3)-4*x^3-4*x,x, algorithm="maxima")

[Out]

-x^4 - 2*x^2 + x*log(3)

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mupad [B]  time = 0.03, size = 14, normalized size = 0.74 \begin {gather*} -x\,\left (x^3+2\,x-\ln \relax (3)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(3) - 4*x - 4*x^3,x)

[Out]

-x*(2*x - log(3) + x^3)

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sympy [A]  time = 0.05, size = 12, normalized size = 0.63 \begin {gather*} - x^{4} - 2 x^{2} + x \log {\relax (3 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(3)-4*x**3-4*x,x)

[Out]

-x**4 - 2*x**2 + x*log(3)

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