3.74.55 \(\int (1+2 e^{16} \log ^2(4)) \, dx\)

Optimal. Leaf size=12 \[ x+2 e^{16} x \log ^2(4) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.08, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \begin {gather*} x \left (1+2 e^{16} \log ^2(4)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + 2*E^16*Log[4]^2,x]

[Out]

x*(1 + 2*E^16*Log[4]^2)

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x \left (1+2 e^{16} \log ^2(4)\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} x+2 e^{16} x \log ^2(4) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + 2*E^16*Log[4]^2,x]

[Out]

x + 2*E^16*x*Log[4]^2

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fricas [A]  time = 0.58, size = 11, normalized size = 0.92 \begin {gather*} 8 \, x e^{16} \log \relax (2)^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*exp(16)*log(2)^2+1,x, algorithm="fricas")

[Out]

8*x*e^16*log(2)^2 + x

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giac [A]  time = 0.19, size = 12, normalized size = 1.00 \begin {gather*} {\left (8 \, e^{16} \log \relax (2)^{2} + 1\right )} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*exp(16)*log(2)^2+1,x, algorithm="giac")

[Out]

(8*e^16*log(2)^2 + 1)*x

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maple [A]  time = 0.01, size = 12, normalized size = 1.00

method	result	size
risch	\(x +8 \ln \relax (2)^{2} x \,{\mathrm e}^{16}\)	\(12\)
default	\(\left (8 \,{\mathrm e}^{16} \ln \relax (2)^{2}+1\right ) x\)	\(13\)
norman	\(\left (8 \,{\mathrm e}^{16} \ln \relax (2)^{2}+1\right ) x\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*exp(16)*ln(2)^2+1,x,method=_RETURNVERBOSE)

[Out]

x+8*ln(2)^2*x*exp(16)

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maxima [A]  time = 0.35, size = 12, normalized size = 1.00 \begin {gather*} {\left (8 \, e^{16} \log \relax (2)^{2} + 1\right )} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*exp(16)*log(2)^2+1,x, algorithm="maxima")

[Out]

(8*e^16*log(2)^2 + 1)*x

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mupad [B]  time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} x\,\left (8\,{\mathrm {e}}^{16}\,{\ln \relax (2)}^2+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*exp(16)*log(2)^2 + 1,x)

[Out]

x*(8*exp(16)*log(2)^2 + 1)

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sympy [A]  time = 0.05, size = 12, normalized size = 1.00 \begin {gather*} x \left (1 + 8 e^{16} \log {\relax (2 )}^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*exp(16)*ln(2)**2+1,x)

[Out]

x*(1 + 8*exp(16)*log(2)**2)

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