3.10.20 \(\int (e^x+2 x+(628+2 x) \log (4)) \, dx\)

Optimal. Leaf size=15 \[ e^x+x^2+(314+x)^2 \log (4) \]

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2194} \begin {gather*} x^2+e^x+(x+314)^2 \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^x + 2*x + (628 + 2*x)*Log[4],x]

[Out]

E^x + x^2 + (314 + x)^2*Log[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} &=x^2+(314+x)^2 \log (4)+\int e^x \, dx\\ &=e^x+x^2+(314+x)^2 \log (4)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 18, normalized size = 1.20 \begin {gather*} e^x+x^2+628 x \log (4)+x^2 \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^x + 2*x + (628 + 2*x)*Log[4],x]

[Out]

E^x + x^2 + 628*x*Log[4] + x^2*Log[4]

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fricas [A]  time = 0.61, size = 17, normalized size = 1.13 \begin {gather*} x^{2} + 2 \, {\left (x^{2} + 628 \, x\right )} \log \relax (2) + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+2*(2*x+628)*log(2)+2*x,x, algorithm="fricas")

[Out]

x^2 + 2*(x^2 + 628*x)*log(2) + e^x

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giac [A]  time = 0.31, size = 17, normalized size = 1.13 \begin {gather*} x^{2} + 2 \, {\left (x^{2} + 628 \, x\right )} \log \relax (2) + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+2*(2*x+628)*log(2)+2*x,x, algorithm="giac")

[Out]

x^2 + 2*(x^2 + 628*x)*log(2) + e^x

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maple [A]  time = 0.02, size = 19, normalized size = 1.27

method	result	size
default	\(x^{2}+2 x^{2} \ln \relax (2)+1256 x \ln \relax (2)+{\mathrm e}^{x}\)	\(19\)
norman	\(\left (1+2 \ln \relax (2)\right ) x^{2}+1256 x \ln \relax (2)+{\mathrm e}^{x}\)	\(19\)
risch	\(x^{2}+2 x^{2} \ln \relax (2)+1256 x \ln \relax (2)+{\mathrm e}^{x}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)+2*(2*x+628)*ln(2)+2*x,x,method=_RETURNVERBOSE)

[Out]

x^2+2*x^2*ln(2)+1256*x*ln(2)+exp(x)

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maxima [A]  time = 0.55, size = 17, normalized size = 1.13 \begin {gather*} x^{2} + 2 \, {\left (x^{2} + 628 \, x\right )} \log \relax (2) + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+2*(2*x+628)*log(2)+2*x,x, algorithm="maxima")

[Out]

x^2 + 2*(x^2 + 628*x)*log(2) + e^x

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mupad [B]  time = 0.64, size = 16, normalized size = 1.07 \begin {gather*} {\mathrm {e}}^x+x^2\,\left (\ln \relax (4)+1\right )+1256\,x\,\ln \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + exp(x) + 2*log(2)*(2*x + 628),x)

[Out]

exp(x) + x^2*(log(4) + 1) + 1256*x*log(2)

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sympy [A]  time = 0.08, size = 19, normalized size = 1.27 \begin {gather*} x^{2} \left (1 + 2 \log {\relax (2 )}\right ) + 1256 x \log {\relax (2 )} + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+2*(2*x+628)*ln(2)+2*x,x)

[Out]

x**2*(1 + 2*log(2)) + 1256*x*log(2) + exp(x)

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