\(\int (4+3 e+24 x+12 x^2+e^4 (12+8 x)) \, dx\) [2180]

Optimal result

Integrand size = 22, antiderivative size = 21 \[ \int \left (4+3 e+24 x+12 x^2+e^4 (12+8 x)\right ) \, dx=\left (e^4+x\right ) \left (-e+4 \left (1+e+3 x+x^2\right )\right ) \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.38, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (4+3 e+24 x+12 x^2+e^4 (12+8 x)\right ) \, dx=4 x^3+12 x^2+(4+3 e) x+e^4 (2 x+3)^2 \]

[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{align*} \text {integral}& = (4+3 e) x+12 x^2+4 x^3+e^4 (3+2 x)^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.52 \[ \int \left (4+3 e+24 x+12 x^2+e^4 (12+8 x)\right ) \, dx=4 x+3 e x+12 e^4 x+12 x^2+4 e^4 x^2+4 x^3 \]

[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

Maple [A] (verified)

Time = 0.05 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.24

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

[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+12*exp(4)+3*exp(1)+12*x+4)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.43 \[ \int \left (4+3 e+24 x+12 x^2+e^4 (12+8 x)\right ) \, dx=4 \, x^{3} + 12 \, x^{2} + 4 \, {\left (x^{2} + 3 \, x\right )} e^{4} + 3 \, x e + 4 \, x \]

[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

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.29 \[ \int \left (4+3 e+24 x+12 x^2+e^4 (12+8 x)\right ) \, dx=4 x^{3} + x^{2} \cdot \left (12 + 4 e^{4}\right ) + x \left (4 + 3 e + 12 e^{4}\right ) \]

[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))

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.43 \[ \int \left (4+3 e+24 x+12 x^2+e^4 (12+8 x)\right ) \, dx=4 \, x^{3} + 12 \, x^{2} + 4 \, {\left (x^{2} + 3 \, x\right )} e^{4} + 3 \, x e + 4 \, x \]

[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

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.43 \[ \int \left (4+3 e+24 x+12 x^2+e^4 (12+8 x)\right ) \, dx=4 \, x^{3} + 12 \, x^{2} + 4 \, {\left (x^{2} + 3 \, x\right )} e^{4} + 3 \, x e + 4 \, x \]

[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

Mupad [B] (verification not implemented)

Time = 8.96 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33 \[ \int \left (4+3 e+24 x+12 x^2+e^4 (12+8 x)\right ) \, dx=4\,x^3+\left (4\,{\mathrm {e}}^4+12\right )\,x^2+\left (3\,\mathrm {e}+12\,{\mathrm {e}}^4+4\right )\,x \]

[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