3.84.39 \(\int (-1-2 x+5 \log (x)) \, dx\)

Optimal. Leaf size=15 \[ -5+x (-1-x+5 (-1+\log (x))) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2295} \begin {gather*} -x^2-6 x+5 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - 2*x + 5*Log[x],x]

[Out]

-6*x - x^2 + 5*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} &=-x-x^2+5 \int \log (x) \, dx\\ &=-6 x-x^2+5 x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} -6 x-x^2+5 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 - 2*x + 5*Log[x],x]

[Out]

-6*x - x^2 + 5*x*Log[x]

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fricas [A]  time = 0.59, size = 14, normalized size = 0.93 \begin {gather*} -x^{2} + 5 \, x \log \relax (x) - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*log(x)-2*x-1,x, algorithm="fricas")

[Out]

-x^2 + 5*x*log(x) - 6*x

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giac [A]  time = 0.20, size = 14, normalized size = 0.93 \begin {gather*} -x^{2} + 5 \, x \log \relax (x) - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*log(x)-2*x-1,x, algorithm="giac")

[Out]

-x^2 + 5*x*log(x) - 6*x

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maple [A]  time = 0.01, size = 15, normalized size = 1.00

method	result	size
default	\(-x^{2}-6 x +5 x \ln \relax (x )\)	\(15\)
norman	\(-x^{2}-6 x +5 x \ln \relax (x )\)	\(15\)
risch	\(-x^{2}-6 x +5 x \ln \relax (x )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*ln(x)-2*x-1,x,method=_RETURNVERBOSE)

[Out]

-x^2-6*x+5*x*ln(x)

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maxima [A]  time = 0.37, size = 14, normalized size = 0.93 \begin {gather*} -x^{2} + 5 \, x \log \relax (x) - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*log(x)-2*x-1,x, algorithm="maxima")

[Out]

-x^2 + 5*x*log(x) - 6*x

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mupad [B]  time = 5.13, size = 10, normalized size = 0.67 \begin {gather*} -x\,\left (x-5\,\ln \relax (x)+6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*log(x) - 2*x - 1,x)

[Out]

-x*(x - 5*log(x) + 6)

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sympy [A]  time = 0.10, size = 12, normalized size = 0.80 \begin {gather*} - x^{2} + 5 x \log {\relax (x )} - 6 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*ln(x)-2*x-1,x)

[Out]

-x**2 + 5*x*log(x) - 6*x

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