3.102.64 \(\int (8 x-4 x^3-\log (x)) \, dx\)

Optimal. Leaf size=19 \[ -9+x-\left (2-x^2\right )^2-x \log (x) \]

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Rubi [A]  time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2295} \begin {gather*} -x^4+4 x^2+x-x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[8*x - 4*x^3 - Log[x],x]

[Out]

x + 4*x^2 - x^4 - x*Log[x]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 17, normalized size = 0.89 \begin {gather*} x+4 x^2-x^4-x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[8*x - 4*x^3 - Log[x],x]

[Out]

x + 4*x^2 - x^4 - x*Log[x]

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fricas [A]  time = 0.57, size = 17, normalized size = 0.89 \begin {gather*} -x^{4} + 4 \, x^{2} - x \log \relax (x) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(x)-4*x^3+8*x,x, algorithm="fricas")

[Out]

-x^4 + 4*x^2 - x*log(x) + x

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giac [A]  time = 0.17, size = 17, normalized size = 0.89 \begin {gather*} -x^{4} + 4 \, x^{2} - x \log \relax (x) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(x)-4*x^3+8*x,x, algorithm="giac")

[Out]

-x^4 + 4*x^2 - x*log(x) + x

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maple [A]  time = 0.03, size = 18, normalized size = 0.95

method	result	size
default	\(-x^{4}+4 x^{2}+x -x \ln \relax (x )\)	\(18\)
norman	\(-x^{4}+4 x^{2}+x -x \ln \relax (x )\)	\(18\)
risch	\(-x^{4}+4 x^{2}+x -x \ln \relax (x )\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-ln(x)-4*x^3+8*x,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.34, size = 17, normalized size = 0.89 \begin {gather*} -x^{4} + 4 \, x^{2} - x \log \relax (x) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(x)-4*x^3+8*x,x, algorithm="maxima")

[Out]

-x^4 + 4*x^2 - x*log(x) + x

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mupad [B]  time = 6.33, size = 16, normalized size = 0.84 \begin {gather*} x\,\left (4\,x-\ln \relax (x)-x^3+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*x - log(x) - 4*x^3,x)

[Out]

x*(4*x - log(x) - x^3 + 1)

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sympy [A]  time = 0.08, size = 14, normalized size = 0.74 \begin {gather*} - x^{4} + 4 x^{2} - x \log {\relax (x )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-ln(x)-4*x**3+8*x,x)

[Out]

-x**4 + 4*x**2 - x*log(x) + x

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