3.51.72 \(\int (e^x+(1-2 x) \log (5)) \, dx\)

Optimal. Leaf size=17 \[ -1+e^x-\left (2-x+x^2\right ) \log (5) \]

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Rubi [A]  time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2194} \begin {gather*} e^x-\frac {1}{4} (1-2 x)^2 \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^x + (1 - 2*x)*Log[5],x]

[Out]

E^x - ((1 - 2*x)^2*Log[5])/4

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} &=-\frac {1}{4} (1-2 x)^2 \log (5)+\int e^x \, dx\\ &=e^x-\frac {1}{4} (1-2 x)^2 \log (5)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 0.88 \begin {gather*} e^x+x \log (5)-x^2 \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^x + (1 - 2*x)*Log[5],x]

[Out]

E^x + x*Log[5] - x^2*Log[5]

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fricas [A]  time = 0.69, size = 14, normalized size = 0.82 \begin {gather*} -{\left (x^{2} - x\right )} \log \relax (5) + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+(1-2*x)*log(5),x, algorithm="fricas")

[Out]

-(x^2 - x)*log(5) + e^x

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giac [A]  time = 0.20, size = 14, normalized size = 0.82 \begin {gather*} -{\left (x^{2} - x\right )} \log \relax (5) + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+(1-2*x)*log(5),x, algorithm="giac")

[Out]

-(x^2 - x)*log(5) + e^x

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maple [A]  time = 0.04, size = 15, normalized size = 0.88

method	result	size
default	\(-x^{2} \ln \relax (5)+x \ln \relax (5)+{\mathrm e}^{x}\)	\(15\)
norman	\(-x^{2} \ln \relax (5)+x \ln \relax (5)+{\mathrm e}^{x}\)	\(15\)
risch	\(-x^{2} \ln \relax (5)+x \ln \relax (5)+{\mathrm e}^{x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)+(1-2*x)*ln(5),x,method=_RETURNVERBOSE)

[Out]

-x^2*ln(5)+x*ln(5)+exp(x)

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maxima [A]  time = 0.35, size = 14, normalized size = 0.82 \begin {gather*} -{\left (x^{2} - x\right )} \log \relax (5) + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+(1-2*x)*log(5),x, algorithm="maxima")

[Out]

-(x^2 - x)*log(5) + e^x

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mupad [B]  time = 0.06, size = 14, normalized size = 0.82 \begin {gather*} {\mathrm {e}}^x+x\,\ln \relax (5)-x^2\,\ln \relax (5) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x) - log(5)*(2*x - 1),x)

[Out]

exp(x) + x*log(5) - x^2*log(5)

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sympy [A]  time = 0.08, size = 14, normalized size = 0.82 \begin {gather*} - x^{2} \log {\relax (5 )} + x \log {\relax (5 )} + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+(1-2*x)*ln(5),x)

[Out]

-x**2*log(5) + x*log(5) + exp(x)

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