3.22.80 \(\int (4+3 e+24 x+12 x^2+e^4 (12+8 x)) \, dx\)

Optimal. Leaf size=21 \[ \left (e^4+x\right ) \left (-e+4 \left (1+e+3 x+x^2\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.38, number of steps used = 1, number of rules used = 0, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 4 x^3+12 x^2+(4+3 e) x+e^4 (2 x+3)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[4 + 3*E + 24*x + 12*x^2 + E^4*(12 + 8*x),x]

[Out]

(4 + 3*E)*x + 12*x^2 + 4*x^3 + E^4*(3 + 2*x)^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=(4+3 e) x+12 x^2+4 x^3+e^4 (3+2 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 32, normalized size = 1.52 \begin {gather*} 4 x+3 e x+12 e^4 x+12 x^2+4 e^4 x^2+4 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[4 + 3*E + 24*x + 12*x^2 + E^4*(12 + 8*x),x]

[Out]

4*x + 3*E*x + 12*E^4*x + 12*x^2 + 4*E^4*x^2 + 4*x^3

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fricas [A]  time = 0.57, size = 30, normalized size = 1.43 \begin {gather*} 4 \, x^{3} + 12 \, x^{2} + 4 \, {\left (x^{2} + 3 \, x\right )} e^{4} + 3 \, x e + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x+12)*exp(4)+3*exp(1)+12*x^2+24*x+4,x, algorithm="fricas")

[Out]

4*x^3 + 12*x^2 + 4*(x^2 + 3*x)*e^4 + 3*x*e + 4*x

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giac [A]  time = 0.37, size = 30, normalized size = 1.43 \begin {gather*} 4 \, x^{3} + 12 \, x^{2} + 4 \, {\left (x^{2} + 3 \, x\right )} e^{4} + 3 \, x e + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x+12)*exp(4)+3*exp(1)+12*x^2+24*x+4,x, algorithm="giac")

[Out]

4*x^3 + 12*x^2 + 4*(x^2 + 3*x)*e^4 + 3*x*e + 4*x

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maple [A]  time = 0.03, size = 26, normalized size = 1.24

method	result	size
gosper	\(x \left (4 x \,{\mathrm e}^{4}+4 x^{2}+3 \,{\mathrm e}+12 \,{\mathrm e}^{4}+12 x +4\right )\)	\(26\)
norman	\(4 x^{3}+\left (4 \,{\mathrm e}^{4}+12\right ) x^{2}+\left (3 \,{\mathrm e}+12 \,{\mathrm e}^{4}+4\right ) x\)	\(29\)
default	\({\mathrm e}^{4} \left (4 x^{2}+12 x \right )+3 x \,{\mathrm e}+4 x^{3}+12 x^{2}+4 x\)	\(32\)
risch	\(4 x^{2} {\mathrm e}^{4}+12 x \,{\mathrm e}^{4}+3 x \,{\mathrm e}+4 x^{3}+12 x^{2}+4 x\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*x+12)*exp(4)+3*exp(1)+12*x^2+24*x+4,x,method=_RETURNVERBOSE)

[Out]

x*(4*x*exp(4)+4*x^2+3*exp(1)+12*exp(4)+12*x+4)

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maxima [A]  time = 0.38, size = 30, normalized size = 1.43 \begin {gather*} 4 \, x^{3} + 12 \, x^{2} + 4 \, {\left (x^{2} + 3 \, x\right )} e^{4} + 3 \, x e + 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x+12)*exp(4)+3*exp(1)+12*x^2+24*x+4,x, algorithm="maxima")

[Out]

4*x^3 + 12*x^2 + 4*(x^2 + 3*x)*e^4 + 3*x*e + 4*x

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mupad [B]  time = 1.19, size = 28, normalized size = 1.33 \begin {gather*} 4\,x^3+\left (4\,{\mathrm {e}}^4+12\right )\,x^2+\left (3\,\mathrm {e}+12\,{\mathrm {e}}^4+4\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(24*x + 3*exp(1) + 12*x^2 + exp(4)*(8*x + 12) + 4,x)

[Out]

x^2*(4*exp(4) + 12) + x*(3*exp(1) + 12*exp(4) + 4) + 4*x^3

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sympy [A]  time = 0.06, size = 27, normalized size = 1.29 \begin {gather*} 4 x^{3} + x^{2} \left (12 + 4 e^{4}\right ) + x \left (4 + 3 e + 12 e^{4}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x+12)*exp(4)+3*exp(1)+12*x**2+24*x+4,x)

[Out]

4*x**3 + x**2*(12 + 4*exp(4)) + x*(4 + 3*E + 12*exp(4))

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