3.74.77 \(\int \frac {16 e^3}{-1+4 x} \, dx\)

Optimal. Leaf size=13 \[ 4 e^3 (-3+\log (5-20 x)) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 31} \begin {gather*} 4 e^3 \log (1-4 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(16*E^3)/(-1 + 4*x),x]

[Out]

4*E^3*Log[1 - 4*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 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (16 e^3\right ) \int \frac {1}{-1+4 x} \, dx\\ &=4 e^3 \log (1-4 x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} 4 e^3 \log (-1+4 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(16*E^3)/(-1 + 4*x),x]

[Out]

4*E^3*Log[-1 + 4*x]

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fricas [A]  time = 0.91, size = 10, normalized size = 0.77 \begin {gather*} 4 \, e^{3} \log \left (4 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16*exp(3)/(4*x-1),x, algorithm="fricas")

[Out]

4*e^3*log(4*x - 1)

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giac [A]  time = 0.16, size = 11, normalized size = 0.85 \begin {gather*} 4 \, e^{3} \log \left ({\left | 4 \, x - 1 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16*exp(3)/(4*x-1),x, algorithm="giac")

[Out]

4*e^3*log(abs(4*x - 1))

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maple [A]  time = 0.15, size = 11, normalized size = 0.85

method	result	size
default	\(4 \,{\mathrm e}^{3} \ln \left (4 x -1\right )\)	\(11\)
norman	\(4 \,{\mathrm e}^{3} \ln \left (4 x -1\right )\)	\(11\)
meijerg	\(4 \,{\mathrm e}^{3} \ln \left (-4 x +1\right )\)	\(11\)
risch	\(4 \,{\mathrm e}^{3} \ln \left (4 x -1\right )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(16*exp(3)/(4*x-1),x,method=_RETURNVERBOSE)

[Out]

4*exp(3)*ln(4*x-1)

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maxima [A]  time = 0.38, size = 10, normalized size = 0.77 \begin {gather*} 4 \, e^{3} \log \left (4 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16*exp(3)/(4*x-1),x, algorithm="maxima")

[Out]

4*e^3*log(4*x - 1)

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mupad [B]  time = 0.06, size = 8, normalized size = 0.62 \begin {gather*} 4\,\ln \left (x-\frac {1}{4}\right )\,{\mathrm {e}}^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*exp(3))/(4*x - 1),x)

[Out]

4*log(x - 1/4)*exp(3)

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sympy [A]  time = 0.05, size = 10, normalized size = 0.77 \begin {gather*} 4 e^{3} \log {\left (4 x - 1 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16*exp(3)/(4*x-1),x)

[Out]

4*exp(3)*log(4*x - 1)

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