3.59.30 \(\int (-e^8+e^3 (1+4 x)) \, dx\)

Optimal. Leaf size=17 \[ -6+e^3 x \left (1-e^5+2 x\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.24, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {1}{8} e^3 (4 x+1)^2-e^8 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^8 + E^3*(1 + 4*x),x]

[Out]

-(E^8*x) + (E^3*(1 + 4*x)^2)/8

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} e^3 \left (x-e^5 x+2 x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^8 + E^3*(1 + 4*x),x]

[Out]

E^3*(x - E^5*x + 2*x^2)

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fricas [A]  time = 0.79, size = 16, normalized size = 0.94 \begin {gather*} -x e^{8} + {\left (2 \, x^{2} + x\right )} e^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)*exp(5)+(4*x+1)*exp(3),x, algorithm="fricas")

[Out]

-x*e^8 + (2*x^2 + x)*e^3

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giac [A]  time = 0.14, size = 16, normalized size = 0.94 \begin {gather*} -x e^{8} + {\left (2 \, x^{2} + x\right )} e^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)*exp(5)+(4*x+1)*exp(3),x, algorithm="giac")

[Out]

-x*e^8 + (2*x^2 + x)*e^3

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maple [A]  time = 0.04, size = 13, normalized size = 0.76

method	result	size
gosper	\(-{\mathrm e}^{3} x \left (-2 x +{\mathrm e}^{5}-1\right )\)	\(13\)
risch	\(-x \,{\mathrm e}^{8}+2 x^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}\)	\(18\)
default	\(-x \,{\mathrm e}^{3} {\mathrm e}^{5}+{\mathrm e}^{3} \left (2 x^{2}+x \right )\)	\(19\)
norman	\(\left (-{\mathrm e}^{3} {\mathrm e}^{5}+{\mathrm e}^{3}\right ) x +2 x^{2} {\mathrm e}^{3}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(3)*exp(5)+(4*x+1)*exp(3),x,method=_RETURNVERBOSE)

[Out]

-exp(3)*x*(-2*x+exp(5)-1)

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maxima [A]  time = 0.36, size = 16, normalized size = 0.94 \begin {gather*} -x e^{8} + {\left (2 \, x^{2} + x\right )} e^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)*exp(5)+(4*x+1)*exp(3),x, algorithm="maxima")

[Out]

-x*e^8 + (2*x^2 + x)*e^3

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mupad [B]  time = 0.07, size = 18, normalized size = 1.06 \begin {gather*} \frac {{\mathrm {e}}^3\,\left (4\,x+1\right )\,\left (4\,x-2\,{\mathrm {e}}^5+1\right )}{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(3)*(4*x + 1) - exp(8),x)

[Out]

(exp(3)*(4*x + 1)*(4*x - 2*exp(5) + 1))/8

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sympy [A]  time = 0.05, size = 15, normalized size = 0.88 \begin {gather*} 2 x^{2} e^{3} + x \left (- e^{8} + e^{3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)*exp(5)+(4*x+1)*exp(3),x)

[Out]

2*x**2*exp(3) + x*(-exp(8) + exp(3))

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