3.61.16 \(\int (17+2 x-2 \log (x)-\log ^2(x)) \, dx\)

Optimal. Leaf size=23 \[ -4+11 x+(3+x)^2+\frac {3}{\log (2)}-x \log ^2(x) \]

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Rubi [A]  time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.61, number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {2295, 2296} \begin {gather*} x^2+17 x-x \log ^2(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[17 + 2*x - 2*Log[x] - Log[x]^2,x]

[Out]

17*x + x^2 - x*Log[x]^2

Rule 2295

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

Rule 2296

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=17 x+x^2-2 \int \log (x) \, dx-\int \log ^2(x) \, dx\\ &=19 x+x^2-2 x \log (x)-x \log ^2(x)+2 \int \log (x) \, dx\\ &=17 x+x^2-x \log ^2(x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.61 \begin {gather*} 17 x+x^2-x \log ^2(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[17 + 2*x - 2*Log[x] - Log[x]^2,x]

[Out]

17*x + x^2 - x*Log[x]^2

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fricas [A]  time = 0.58, size = 14, normalized size = 0.61 \begin {gather*} -x \log \relax (x)^{2} + x^{2} + 17 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(x)^2-2*log(x)+2*x+17,x, algorithm="fricas")

[Out]

-x*log(x)^2 + x^2 + 17*x

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giac [A]  time = 0.13, size = 14, normalized size = 0.61 \begin {gather*} -x \log \relax (x)^{2} + x^{2} + 17 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(x)^2-2*log(x)+2*x+17,x, algorithm="giac")

[Out]

-x*log(x)^2 + x^2 + 17*x

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maple [A]  time = 0.02, size = 15, normalized size = 0.65

method	result	size
default	\(x^{2}+17 x -x \ln \relax (x )^{2}\)	\(15\)
norman	\(x^{2}+17 x -x \ln \relax (x )^{2}\)	\(15\)
risch	\(x^{2}+17 x -x \ln \relax (x )^{2}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-ln(x)^2-2*ln(x)+2*x+17,x,method=_RETURNVERBOSE)

[Out]

x^2+17*x-x*ln(x)^2

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maxima [A]  time = 0.34, size = 25, normalized size = 1.09 \begin {gather*} -{\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x + x^{2} - 2 \, x \log \relax (x) + 19 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-log(x)^2-2*log(x)+2*x+17,x, algorithm="maxima")

[Out]

-(log(x)^2 - 2*log(x) + 2)*x + x^2 - 2*x*log(x) + 19*x

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mupad [B]  time = 4.23, size = 11, normalized size = 0.48 \begin {gather*} x\,\left (-{\ln \relax (x)}^2+x+17\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x - 2*log(x) - log(x)^2 + 17,x)

[Out]

x*(x - log(x)^2 + 17)

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sympy [A]  time = 0.09, size = 12, normalized size = 0.52 \begin {gather*} x^{2} - x \log {\relax (x )}^{2} + 17 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-ln(x)**2-2*ln(x)+2*x+17,x)

[Out]

x**2 - x*log(x)**2 + 17*x

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