3.38.5 \(\int (-60+50 x-25 \log (x)) \, dx\)

Optimal. Leaf size=14 \[ 5 x (3+5 (-2+x-\log (x))) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, 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*} 25 x^2-35 x-25 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-60 + 50*x - 25*Log[x],x]

[Out]

-35*x + 25*x^2 - 25*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} &=-60 x+25 x^2-25 \int \log (x) \, dx\\ &=-35 x+25 x^2-25 x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -35 x+25 x^2-25 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-60 + 50*x - 25*Log[x],x]

[Out]

-35*x + 25*x^2 - 25*x*Log[x]

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fricas [A]  time = 0.70, size = 14, normalized size = 1.00 \begin {gather*} 25 \, x^{2} - 25 \, x \log \relax (x) - 35 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-25*log(x)+50*x-60,x, algorithm="fricas")

[Out]

25*x^2 - 25*x*log(x) - 35*x

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giac [A]  time = 0.18, size = 14, normalized size = 1.00 \begin {gather*} 25 \, x^{2} - 25 \, x \log \relax (x) - 35 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-25*log(x)+50*x-60,x, algorithm="giac")

[Out]

25*x^2 - 25*x*log(x) - 35*x

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maple [A]  time = 0.01, size = 15, normalized size = 1.07

method	result	size
default	\(25 x^{2}-35 x -25 x \ln \relax (x )\)	\(15\)
norman	\(25 x^{2}-35 x -25 x \ln \relax (x )\)	\(15\)
risch	\(25 x^{2}-35 x -25 x \ln \relax (x )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-25*ln(x)+50*x-60,x,method=_RETURNVERBOSE)

[Out]

25*x^2-35*x-25*x*ln(x)

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maxima [A]  time = 0.37, size = 14, normalized size = 1.00 \begin {gather*} 25 \, x^{2} - 25 \, x \log \relax (x) - 35 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-25*log(x)+50*x-60,x, algorithm="maxima")

[Out]

25*x^2 - 25*x*log(x) - 35*x

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mupad [B]  time = 2.14, size = 12, normalized size = 0.86 \begin {gather*} -5\,x\,\left (5\,\ln \relax (x)-5\,x+7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(50*x - 25*log(x) - 60,x)

[Out]

-5*x*(5*log(x) - 5*x + 7)

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sympy [A]  time = 0.09, size = 14, normalized size = 1.00 \begin {gather*} 25 x^{2} - 25 x \log {\relax (x )} - 35 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-25*ln(x)+50*x-60,x)

[Out]

25*x**2 - 25*x*log(x) - 35*x

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