3.34.43 \(\int \frac {230+50 \log (3 x)}{x} \, dx\) [3343]

Optimal. Leaf size=12 \[ (-3-5 (4+\log (3 x)))^2 \]

[Out]

(-23-5*ln(3*x))^2

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Rubi [A]
time = 0.01, antiderivative size = 10, normalized size of antiderivative = 0.83, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2338} \begin {gather*} (5 \log (3 x)+23)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(230 + 50*Log[3*x])/x,x]

[Out]

(23 + 5*Log[3*x])^2

Rule 2338

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=(23+5 \log (3 x))^2\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.08 \begin {gather*} 230 \log (x)+25 \log ^2(3 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(230 + 50*Log[3*x])/x,x]

[Out]

230*Log[x] + 25*Log[3*x]^2

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Maple [A]
time = 0.15, size = 16, normalized size = 1.33

method	result	size
risch	\(25 \ln \left (3 x \right )^{2}+230 \ln \left (x \right )\)	\(14\)
derivativedivides	\(25 \ln \left (3 x \right )^{2}+230 \ln \left (3 x \right )\)	\(16\)
default	\(25 \ln \left (3 x \right )^{2}+230 \ln \left (3 x \right )\)	\(16\)
norman	\(25 \ln \left (3 x \right )^{2}+230 \ln \left (3 x \right )\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((50*ln(3*x)+230)/x,x,method=_RETURNVERBOSE)

[Out]

25*ln(3*x)^2+230*ln(3*x)

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Maxima [A]
time = 0.26, size = 10, normalized size = 0.83 \begin {gather*} {\left (5 \, \log \left (3 \, x\right ) + 23\right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((50*log(3*x)+230)/x,x, algorithm="maxima")

[Out]

(5*log(3*x) + 23)^2

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Fricas [A]
time = 0.41, size = 15, normalized size = 1.25 \begin {gather*} 25 \, \log \left (3 \, x\right )^{2} + 230 \, \log \left (3 \, x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((50*log(3*x)+230)/x,x, algorithm="fricas")

[Out]

25*log(3*x)^2 + 230*log(3*x)

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Sympy [A]
time = 0.03, size = 12, normalized size = 1.00 \begin {gather*} 230 \log {\left (x \right )} + 25 \log {\left (3 x \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((50*ln(3*x)+230)/x,x)

[Out]

230*log(x) + 25*log(3*x)**2

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Giac [A]
time = 0.43, size = 13, normalized size = 1.08 \begin {gather*} 25 \, \log \left (3 \, x\right )^{2} + 230 \, \log \left (x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((50*log(3*x)+230)/x,x, algorithm="giac")

[Out]

25*log(3*x)^2 + 230*log(x)

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Mupad [B]
time = 1.91, size = 14, normalized size = 1.17 \begin {gather*} 5\,\ln \left (x\right )\,\left (10\,\ln \left (3\right )+5\,\ln \left (x\right )+46\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((50*log(3*x) + 230)/x,x)

[Out]

5*log(x)*(10*log(3) + 5*log(x) + 46)

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