3.20.90 \(\int \frac {1}{10} (-629+320 x-160 \log (x)) \, dx\)

Optimal. Leaf size=17 \[ -3+\frac {11 x}{10}+16 x (-3+x-\log (x)) \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2295} \begin {gather*} 16 x^2-\frac {469 x}{10}-16 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-629 + 320*x - 160*Log[x])/10,x]

[Out]

(-469*x)/10 + 16*x^2 - 16*x*Log[x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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} &=\frac {1}{10} \int (-629+320 x-160 \log (x)) \, dx\\ &=-\frac {629 x}{10}+16 x^2-16 \int \log (x) \, dx\\ &=-\frac {469 x}{10}+16 x^2-16 x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.94 \begin {gather*} -\frac {469 x}{10}+16 x^2-16 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-629 + 320*x - 160*Log[x])/10,x]

[Out]

(-469*x)/10 + 16*x^2 - 16*x*Log[x]

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fricas [A]  time = 0.62, size = 14, normalized size = 0.82 \begin {gather*} 16 \, x^{2} - 16 \, x \log \relax (x) - \frac {469}{10} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*log(x)+32*x-629/10,x, algorithm="fricas")

[Out]

16*x^2 - 16*x*log(x) - 469/10*x

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giac [A]  time = 0.21, size = 14, normalized size = 0.82 \begin {gather*} 16 \, x^{2} - 16 \, x \log \relax (x) - \frac {469}{10} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*log(x)+32*x-629/10,x, algorithm="giac")

[Out]

16*x^2 - 16*x*log(x) - 469/10*x

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maple [A]  time = 0.02, size = 15, normalized size = 0.88

method	result	size
default	\(-\frac {469 x}{10}+16 x^{2}-16 x \ln \relax (x )\)	\(15\)
norman	\(-\frac {469 x}{10}+16 x^{2}-16 x \ln \relax (x )\)	\(15\)
risch	\(-\frac {469 x}{10}+16 x^{2}-16 x \ln \relax (x )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-16*ln(x)+32*x-629/10,x,method=_RETURNVERBOSE)

[Out]

-469/10*x+16*x^2-16*x*ln(x)

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maxima [A]  time = 0.35, size = 14, normalized size = 0.82 \begin {gather*} 16 \, x^{2} - 16 \, x \log \relax (x) - \frac {469}{10} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*log(x)+32*x-629/10,x, algorithm="maxima")

[Out]

16*x^2 - 16*x*log(x) - 469/10*x

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mupad [B]  time = 1.12, size = 12, normalized size = 0.71 \begin {gather*} -\frac {x\,\left (160\,\ln \relax (x)-160\,x+469\right )}{10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x - 16*log(x) - 629/10,x)

[Out]

-(x*(160*log(x) - 160*x + 469))/10

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sympy [A]  time = 0.09, size = 15, normalized size = 0.88 \begin {gather*} 16 x^{2} - 16 x \log {\relax (x )} - \frac {469 x}{10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*ln(x)+32*x-629/10,x)

[Out]

16*x**2 - 16*x*log(x) - 469*x/10

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