3.96.93 \(\int e^4 (-2+4 x) \, dx\)

Optimal. Leaf size=26 \[ \frac {e^4 \left (x-2 x \left (x-x \left (\frac {1}{9 x}+x\right )\right )\right )}{x} \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.54, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \begin {gather*} \frac {1}{2} e^4 (1-2 x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^4*(-2 + 4*x),x]

[Out]

(E^4*(1 - 2*x)^2)/2

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} e^4 (1-2 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.50 \begin {gather*} e^4 \left (-2 x+2 x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^4*(-2 + 4*x),x]

[Out]

E^4*(-2*x + 2*x^2)

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fricas [A]  time = 0.62, size = 11, normalized size = 0.42 \begin {gather*} 2 \, {\left (x^{2} - x\right )} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*(x^2 - x)*e^4

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giac [A]  time = 0.17, size = 11, normalized size = 0.42 \begin {gather*} 2 \, {\left (x^{2} - x\right )} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*(x^2 - x)*e^4

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maple [A]  time = 0.02, size = 9, normalized size = 0.35

method	result	size
gosper	\(2 \,{\mathrm e}^{4} x \left (x -1\right )\)	\(9\)
default	\(\left (2 x^{2}-2 x \right ) {\mathrm e}^{4}\)	\(13\)
norman	\(-2 x \,{\mathrm e}^{4}+2 x^{2} {\mathrm e}^{4}\)	\(14\)
risch	\(-2 x \,{\mathrm e}^{4}+2 x^{2} {\mathrm e}^{4}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*exp(4)*x*(x-1)

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maxima [A]  time = 0.36, size = 11, normalized size = 0.42 \begin {gather*} 2 \, {\left (x^{2} - x\right )} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*(x^2 - x)*e^4

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mupad [B]  time = 0.11, size = 11, normalized size = 0.42 \begin {gather*} \frac {{\mathrm {e}}^4\,{\left (2\,x-1\right )}^2}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(4)*(4*x - 2),x)

[Out]

(exp(4)*(2*x - 1)^2)/2

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sympy [A]  time = 0.05, size = 14, normalized size = 0.54 \begin {gather*} 2 x^{2} e^{4} - 2 x e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x**2*exp(4) - 2*x*exp(4)

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