3.84.98 \(\int (1+e^5 (-1-3 x^2)) \, dx\)

Optimal. Leaf size=19 \[ -6-e^5 x \left (1+x^2\right )+\log \left (3 e^x\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.84, number of steps used = 2, number of rules used = 0, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -e^5 x^3-e^5 x+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + E^5*(-1 - 3*x^2),x]

[Out]

x - E^5*x - E^5*x^3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x+e^5 \int \left (-1-3 x^2\right ) \, dx\\ &=x-e^5 x-e^5 x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.84 \begin {gather*} x-e^5 x-e^5 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + E^5*(-1 - 3*x^2),x]

[Out]

x - E^5*x - E^5*x^3

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fricas [A]  time = 0.56, size = 11, normalized size = 0.58 \begin {gather*} -{\left (x^{3} + x\right )} e^{5} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^2-1)*exp(5)+1,x, algorithm="fricas")

[Out]

-(x^3 + x)*e^5 + x

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giac [A]  time = 0.15, size = 11, normalized size = 0.58 \begin {gather*} -{\left (x^{3} + x\right )} e^{5} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^2-1)*exp(5)+1,x, algorithm="giac")

[Out]

-(x^3 + x)*e^5 + x

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maple [A]  time = 0.02, size = 14, normalized size = 0.74

method	result	size
gosper	\(-x \left (x^{2} {\mathrm e}^{5}+{\mathrm e}^{5}-1\right )\)	\(14\)
default	\({\mathrm e}^{5} \left (-x^{3}-x \right )+x\)	\(15\)
risch	\(-x^{3} {\mathrm e}^{5}-x \,{\mathrm e}^{5}+x\)	\(15\)
norman	\(\left (1-{\mathrm e}^{5}\right ) x -x^{3} {\mathrm e}^{5}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-3*x^2-1)*exp(5)+1,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.35, size = 11, normalized size = 0.58 \begin {gather*} -{\left (x^{3} + x\right )} e^{5} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^2-1)*exp(5)+1,x, algorithm="maxima")

[Out]

-(x^3 + x)*e^5 + x

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mupad [B]  time = 5.61, size = 15, normalized size = 0.79 \begin {gather*} -{\mathrm {e}}^5\,x^3+\left (1-{\mathrm {e}}^5\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - exp(5)*(3*x^2 + 1),x)

[Out]

- x*(exp(5) - 1) - x^3*exp(5)

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sympy [A]  time = 0.05, size = 12, normalized size = 0.63 \begin {gather*} - x^{3} e^{5} + x \left (1 - e^{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x**3*exp(5) + x*(1 - exp(5))

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