3.42.42 \(\int (8+5 \log (4 x)) \, dx\)

Optimal. Leaf size=17 \[ 2 \left (6+\frac {3 x}{2}\right )+5 x \log (4 x) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.65, number of steps used = 2, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2295} \begin {gather*} 3 x+5 x \log (4 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[8 + 5*Log[4*x],x]

[Out]

3*x + 5*x*Log[4*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} &=8 x+5 \int \log (4 x) \, dx\\ &=3 x+5 x \log (4 x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.65 \begin {gather*} 3 x+5 x \log (4 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[8 + 5*Log[4*x],x]

[Out]

3*x + 5*x*Log[4*x]

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fricas [A]  time = 0.85, size = 11, normalized size = 0.65 \begin {gather*} 5 \, x \log \left (4 \, x\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*log(4*x)+8,x, algorithm="fricas")

[Out]

5*x*log(4*x) + 3*x

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giac [A]  time = 0.18, size = 11, normalized size = 0.65 \begin {gather*} 5 \, x \log \left (4 \, x\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*log(4*x)+8,x, algorithm="giac")

[Out]

5*x*log(4*x) + 3*x

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maple [A]  time = 0.01, size = 12, normalized size = 0.71

method	result	size
derivativedivides	\(3 x +5 x \ln \left (4 x \right )\)	\(12\)
default	\(3 x +5 x \ln \left (4 x \right )\)	\(12\)
norman	\(3 x +5 x \ln \left (4 x \right )\)	\(12\)
risch	\(3 x +5 x \ln \left (4 x \right )\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*ln(4*x)+8,x,method=_RETURNVERBOSE)

[Out]

3*x+5*x*ln(4*x)

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maxima [A]  time = 0.36, size = 11, normalized size = 0.65 \begin {gather*} 5 \, x \log \left (4 \, x\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*log(4*x)+8,x, algorithm="maxima")

[Out]

5*x*log(4*x) + 3*x

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mupad [B]  time = 3.31, size = 10, normalized size = 0.59 \begin {gather*} x\,\left (5\,\ln \left (4\,x\right )+3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*log(4*x) + 8,x)

[Out]

x*(5*log(4*x) + 3)

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sympy [A]  time = 0.08, size = 10, normalized size = 0.59 \begin {gather*} 5 x \log {\left (4 x \right )} + 3 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*ln(4*x)+8,x)

[Out]

5*x*log(4*x) + 3*x

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