3.51.21 \(\int (25+25 e^x-25 \log (3)) \, dx\)

Optimal. Leaf size=19 \[ -25 \left (e+e^3-e^x-x+x \log (3)\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2194} \begin {gather*} 25 e^x+25 x (1-\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[25 + 25*E^x - 25*Log[3],x]

[Out]

25*E^x + 25*x*(1 - Log[3])

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} &=25 x (1-\log (3))+25 \int e^x \, dx\\ &=25 e^x+25 x (1-\log (3))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.63 \begin {gather*} 25 \left (e^x+x-x \log (3)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[25 + 25*E^x - 25*Log[3],x]

[Out]

25*(E^x + x - x*Log[3])

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fricas [A]  time = 0.79, size = 13, normalized size = 0.68 \begin {gather*} -25 \, x \log \relax (3) + 25 \, x + 25 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(25*exp(x)-25*log(3)+25,x, algorithm="fricas")

[Out]

-25*x*log(3) + 25*x + 25*e^x

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giac [A]  time = 0.20, size = 13, normalized size = 0.68 \begin {gather*} -25 \, x \log \relax (3) + 25 \, x + 25 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(25*exp(x)-25*log(3)+25,x, algorithm="giac")

[Out]

-25*x*log(3) + 25*x + 25*e^x

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maple [A]  time = 0.04, size = 14, normalized size = 0.74

method	result	size
default	\(25 \,{\mathrm e}^{x}+25 x -25 x \ln \relax (3)\)	\(14\)
norman	\(\left (-25 \ln \relax (3)+25\right ) x +25 \,{\mathrm e}^{x}\)	\(14\)
risch	\(25 \,{\mathrm e}^{x}+25 x -25 x \ln \relax (3)\)	\(14\)
derivativedivides	\(25 \,{\mathrm e}^{x}+25 \left (1-\ln \relax (3)\right ) \ln \left ({\mathrm e}^{x}\right )\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(25*exp(x)-25*ln(3)+25,x,method=_RETURNVERBOSE)

[Out]

25*exp(x)+25*x-25*x*ln(3)

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maxima [A]  time = 0.35, size = 13, normalized size = 0.68 \begin {gather*} -25 \, x \log \relax (3) + 25 \, x + 25 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(25*exp(x)-25*log(3)+25,x, algorithm="maxima")

[Out]

-25*x*log(3) + 25*x + 25*e^x

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mupad [B]  time = 0.05, size = 14, normalized size = 0.74 \begin {gather*} 25\,{\mathrm {e}}^x-x\,\left (25\,\ln \relax (3)-25\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(25*exp(x) - 25*log(3) + 25,x)

[Out]

25*exp(x) - x*(25*log(3) - 25)

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sympy [A]  time = 0.07, size = 12, normalized size = 0.63 \begin {gather*} x \left (25 - 25 \log {\relax (3 )}\right ) + 25 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(25*exp(x)-25*ln(3)+25,x)

[Out]

x*(25 - 25*log(3)) + 25*exp(x)

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