3.78.66 \(\int (2+2 x+e (20 x-4 x^3)) \, dx\)

Optimal. Leaf size=22 \[ 3-2 x+x (4+x)-e \left (5-x^2\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.86, number of steps used = 2, number of rules used = 0, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -e x^4+10 e x^2+x^2+2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2 + 2*x + E*(20*x - 4*x^3),x]

[Out]

2*x + x^2 + 10*E*x^2 - E*x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 x+x^2+e \int \left (20 x-4 x^3\right ) \, dx\\ &=2 x+x^2+10 e x^2-e x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 0.86 \begin {gather*} 2 x+(1+10 e) x^2-e x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2 + 2*x + E*(20*x - 4*x^3),x]

[Out]

2*x + (1 + 10*E)*x^2 - E*x^4

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fricas [A]  time = 0.61, size = 20, normalized size = 0.91 \begin {gather*} x^{2} - {\left (x^{4} - 10 \, x^{2}\right )} e + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x^3+20*x)*exp(1)+2*x+2,x, algorithm="fricas")

[Out]

x^2 - (x^4 - 10*x^2)*e + 2*x

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giac [A]  time = 0.21, size = 20, normalized size = 0.91 \begin {gather*} x^{2} - {\left (x^{4} - 10 \, x^{2}\right )} e + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x^3+20*x)*exp(1)+2*x+2,x, algorithm="giac")

[Out]

x^2 - (x^4 - 10*x^2)*e + 2*x

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maple [A]  time = 0.02, size = 20, normalized size = 0.91

method	result	size
gosper	\(-x \left (x^{3} {\mathrm e}-10 x \,{\mathrm e}-x -2\right )\)	\(20\)
default	\({\mathrm e} \left (-x^{4}+10 x^{2}\right )+x^{2}+2 x\)	\(22\)
norman	\(\left (10 \,{\mathrm e}+1\right ) x^{2}+2 x -x^{4} {\mathrm e}\)	\(22\)
risch	\(-x^{4} {\mathrm e}+10 x^{2} {\mathrm e}+x^{2}+2 x\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*x^3+20*x)*exp(1)+2*x+2,x,method=_RETURNVERBOSE)

[Out]

-x*(x^3*exp(1)-10*x*exp(1)-x-2)

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maxima [A]  time = 0.35, size = 20, normalized size = 0.91 \begin {gather*} x^{2} - {\left (x^{4} - 10 \, x^{2}\right )} e + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x^3+20*x)*exp(1)+2*x+2,x, algorithm="maxima")

[Out]

x^2 - (x^4 - 10*x^2)*e + 2*x

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mupad [B]  time = 0.04, size = 21, normalized size = 0.95 \begin {gather*} -\mathrm {e}\,x^4+\left (10\,\mathrm {e}+1\right )\,x^2+2\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + exp(1)*(20*x - 4*x^3) + 2,x)

[Out]

2*x + x^2*(10*exp(1) + 1) - x^4*exp(1)

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sympy [A]  time = 0.05, size = 19, normalized size = 0.86 \begin {gather*} - e x^{4} + x^{2} \left (1 + 10 e\right ) + 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x**3+20*x)*exp(1)+2*x+2,x)

[Out]

-E*x**4 + x**2*(1 + 10*E) + 2*x

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