3.5.43 \(\int (-4+e^x+\log (16)) \, dx\)

Optimal. Leaf size=14 \[ -1+e^x-x+x (-3+\log (16)) \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2194} \begin {gather*} e^x-x (4-\log (16)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-4 + E^x + Log[16],x]

[Out]

E^x - x*(4 - Log[16])

Rule 2194

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

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.79 \begin {gather*} e^x-4 x+x \log (16) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-4 + E^x + Log[16],x]

[Out]

E^x - 4*x + x*Log[16]

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fricas [A]  time = 1.03, size = 11, normalized size = 0.79 \begin {gather*} 4 \, x \log \relax (2) - 4 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+4*log(2)-4,x, algorithm="fricas")

[Out]

4*x*log(2) - 4*x + e^x

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giac [A]  time = 0.21, size = 11, normalized size = 0.79 \begin {gather*} 4 \, x \log \relax (2) - 4 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+4*log(2)-4,x, algorithm="giac")

[Out]

4*x*log(2) - 4*x + e^x

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maple [A]  time = 0.03, size = 12, normalized size = 0.86

method	result	size
default	\(-4 x +4 x \ln \relax (2)+{\mathrm e}^{x}\)	\(12\)
norman	\(\left (4 \ln \relax (2)-4\right ) x +{\mathrm e}^{x}\)	\(12\)
risch	\(-4 x +4 x \ln \relax (2)+{\mathrm e}^{x}\)	\(12\)
derivativedivides	\({\mathrm e}^{x}+\left (4 \ln \relax (2)-4\right ) \ln \left ({\mathrm e}^{x}\right )\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)+4*ln(2)-4,x,method=_RETURNVERBOSE)

[Out]

-4*x+4*x*ln(2)+exp(x)

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maxima [A]  time = 0.35, size = 11, normalized size = 0.79 \begin {gather*} 4 \, x \log \relax (2) - 4 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+4*log(2)-4,x, algorithm="maxima")

[Out]

4*x*log(2) - 4*x + e^x

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mupad [B]  time = 0.04, size = 9, normalized size = 0.64 \begin {gather*} {\mathrm {e}}^x+x\,\left (\ln \left (16\right )-4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*log(2) + exp(x) - 4,x)

[Out]

exp(x) + x*(log(16) - 4)

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sympy [A]  time = 0.08, size = 10, normalized size = 0.71 \begin {gather*} x \left (-4 + 4 \log {\relax (2 )}\right ) + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+4*ln(2)-4,x)

[Out]

x*(-4 + 4*log(2)) + exp(x)

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