3.44.6 \(\int (1+e^3 (1-4 x)-2 x+6 x^2) \, dx\)

Optimal. Leaf size=21 \[ x+\left (e^3-x\right ) (-x+(2-2 x) x) \]

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Rubi [A]  time = 0.00, antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps used = 1, number of rules used = 0, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 2 x^3-x^2+x-\frac {1}{8} e^3 (1-4 x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + E^3*(1 - 4*x) - 2*x + 6*x^2,x]

[Out]

-1/8*(E^3*(1 - 4*x)^2) + x - x^2 + 2*x^3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{8} e^3 (1-4 x)^2+x-x^2+2 x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 25, normalized size = 1.19 \begin {gather*} x+e^3 x-x^2-2 e^3 x^2+2 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + E^3*(1 - 4*x) - 2*x + 6*x^2,x]

[Out]

x + E^3*x - x^2 - 2*E^3*x^2 + 2*x^3

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fricas [A]  time = 0.64, size = 25, normalized size = 1.19 \begin {gather*} 2 \, x^{3} - x^{2} - {\left (2 \, x^{2} - x\right )} e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+1)*exp(3)+6*x^2-2*x+1,x, algorithm="fricas")

[Out]

2*x^3 - x^2 - (2*x^2 - x)*e^3 + x

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giac [A]  time = 0.14, size = 25, normalized size = 1.19 \begin {gather*} 2 \, x^{3} - x^{2} - {\left (2 \, x^{2} - x\right )} e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+1)*exp(3)+6*x^2-2*x+1,x, algorithm="giac")

[Out]

2*x^3 - x^2 - (2*x^2 - x)*e^3 + x

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maple [A]  time = 0.02, size = 21, normalized size = 1.00

method	result	size
gosper	\(-x \left (2 x \,{\mathrm e}^{3}-2 x^{2}-{\mathrm e}^{3}+x -1\right )\)	\(21\)
default	\({\mathrm e}^{3} \left (-2 x^{2}+x \right )+2 x^{3}-x^{2}+x\)	\(23\)
norman	\(\left (-2 \,{\mathrm e}^{3}-1\right ) x^{2}+\left ({\mathrm e}^{3}+1\right ) x +2 x^{3}\)	\(23\)
risch	\(-2 x^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}+2 x^{3}-x^{2}+x\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*x+1)*exp(3)+6*x^2-2*x+1,x,method=_RETURNVERBOSE)

[Out]

-x*(2*x*exp(3)-2*x^2-exp(3)+x-1)

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maxima [A]  time = 0.34, size = 25, normalized size = 1.19 \begin {gather*} 2 \, x^{3} - x^{2} - {\left (2 \, x^{2} - x\right )} e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+1)*exp(3)+6*x^2-2*x+1,x, algorithm="maxima")

[Out]

2*x^3 - x^2 - (2*x^2 - x)*e^3 + x

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mupad [B]  time = 3.10, size = 23, normalized size = 1.10 \begin {gather*} 2\,x^3+\left (-2\,{\mathrm {e}}^3-1\right )\,x^2+\left ({\mathrm {e}}^3+1\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x^2 - 2*x - exp(3)*(4*x - 1) + 1,x)

[Out]

x*(exp(3) + 1) - x^2*(2*exp(3) + 1) + 2*x^3

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sympy [A]  time = 0.07, size = 22, normalized size = 1.05 \begin {gather*} 2 x^{3} + x^{2} \left (- 2 e^{3} - 1\right ) + x \left (1 + e^{3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+1)*exp(3)+6*x**2-2*x+1,x)

[Out]

2*x**3 + x**2*(-2*exp(3) - 1) + x*(1 + exp(3))

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