3.12.96 \(\int \frac {2 e^{16}}{x} \, dx\)

Optimal. Leaf size=8 \[ e^{16} \log \left (x^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.88, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 29} \begin {gather*} 2 e^{16} \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2*E^16)/x,x]

[Out]

2*E^16*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 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (2 e^{16}\right ) \int \frac {1}{x} \, dx\\ &=2 e^{16} \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.88 \begin {gather*} 2 e^{16} \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*E^16)/x,x]

[Out]

2*E^16*Log[x]

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fricas [A]  time = 1.08, size = 6, normalized size = 0.75 \begin {gather*} 2 \, e^{16} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(3)^2*exp(5)^2/x,x, algorithm="fricas")

[Out]

2*e^16*log(x)

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giac [A]  time = 0.23, size = 7, normalized size = 0.88 \begin {gather*} 2 \, e^{16} \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(3)^2*exp(5)^2/x,x, algorithm="giac")

[Out]

2*e^16*log(abs(x))

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maple [A]  time = 0.02, size = 7, normalized size = 0.88

method	result	size
risch	\(2 \,{\mathrm e}^{16} \ln \relax (x )\)	\(7\)
default	\(2 \,{\mathrm e}^{6} {\mathrm e}^{10} \ln \relax (x )\)	\(13\)
norman	\(2 \,{\mathrm e}^{6} {\mathrm e}^{10} \ln \relax (x )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(3)^2*exp(5)^2/x,x,method=_RETURNVERBOSE)

[Out]

2*exp(16)*ln(x)

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maxima [A]  time = 0.46, size = 6, normalized size = 0.75 \begin {gather*} 2 \, e^{16} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(3)^2*exp(5)^2/x,x, algorithm="maxima")

[Out]

2*e^16*log(x)

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mupad [B]  time = 0.02, size = 6, normalized size = 0.75 \begin {gather*} 2\,{\mathrm {e}}^{16}\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(16))/x,x)

[Out]

2*exp(16)*log(x)

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sympy [A]  time = 0.05, size = 7, normalized size = 0.88 \begin {gather*} 2 e^{16} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(3)**2*exp(5)**2/x,x)

[Out]

2*exp(16)*log(x)

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