3.63.85 \(\int (1-13 x-2 x \log (x)) \, dx\)

Optimal. Leaf size=15 \[ -14+x-6 x^2-x^2 \log (x) \]

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Rubi [A]  time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2304} \begin {gather*} -6 x^2+x^2 (-\log (x))+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 - 13*x - 2*x*Log[x],x]

[Out]

x - 6*x^2 - x^2*Log[x]

Rule 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x-\frac {13 x^2}{2}-2 \int x \log (x) \, dx\\ &=x-6 x^2-x^2 \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} x-6 x^2-x^2 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 - 13*x - 2*x*Log[x],x]

[Out]

x - 6*x^2 - x^2*Log[x]

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fricas [A]  time = 0.61, size = 14, normalized size = 0.93 \begin {gather*} -x^{2} \log \relax (x) - 6 \, x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*x*log(x)-13*x+1,x, algorithm="fricas")

[Out]

-x^2*log(x) - 6*x^2 + x

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giac [A]  time = 0.22, size = 14, normalized size = 0.93 \begin {gather*} -x^{2} \log \relax (x) - 6 \, x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*x*log(x)-13*x+1,x, algorithm="giac")

[Out]

-x^2*log(x) - 6*x^2 + x

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maple [A]  time = 0.02, size = 15, normalized size = 1.00

method	result	size
default	\(x -6 x^{2}-x^{2} \ln \relax (x )\)	\(15\)
norman	\(x -6 x^{2}-x^{2} \ln \relax (x )\)	\(15\)
risch	\(x -6 x^{2}-x^{2} \ln \relax (x )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*x*ln(x)-13*x+1,x,method=_RETURNVERBOSE)

[Out]

x-6*x^2-x^2*ln(x)

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maxima [A]  time = 0.38, size = 14, normalized size = 0.93 \begin {gather*} -x^{2} \log \relax (x) - 6 \, x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*x*log(x)-13*x+1,x, algorithm="maxima")

[Out]

-x^2*log(x) - 6*x^2 + x

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mupad [B]  time = 4.21, size = 12, normalized size = 0.80 \begin {gather*} -x\,\left (6\,x+x\,\ln \relax (x)-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - 2*x*log(x) - 13*x,x)

[Out]

-x*(6*x + x*log(x) - 1)

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sympy [A]  time = 0.08, size = 12, normalized size = 0.80 \begin {gather*} - x^{2} \log {\relax (x )} - 6 x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*x*ln(x)-13*x+1,x)

[Out]

-x**2*log(x) - 6*x**2 + x

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