3.78.74 \(\int \frac {-3+400 e^{e^5}-2 x^2}{x^2} \, dx\)

Optimal. Leaf size=27 \[ 4+16 \left (4+e^{e^5} \left (3-\frac {25}{x}\right )\right )+\frac {3}{x}-2 x \]

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Rubi [A]  time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.63, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \begin {gather*} \frac {3-400 e^{e^5}}{x}-2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-3 + 400*E^E^5 - 2*x^2)/x^2,x]

[Out]

(3 - 400*E^E^5)/x - 2*x

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2+\frac {-3+400 e^{e^5}}{x^2}\right ) \, dx\\ &=\frac {3-400 e^{e^5}}{x}-2 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 18, normalized size = 0.67 \begin {gather*} -\frac {-3+400 e^{e^5}}{x}-2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3 + 400*E^E^5 - 2*x^2)/x^2,x]

[Out]

-((-3 + 400*E^E^5)/x) - 2*x

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fricas [A]  time = 0.79, size = 17, normalized size = 0.63 \begin {gather*} -\frac {2 \, x^{2} + 400 \, e^{\left (e^{5}\right )} - 3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((400*exp(exp(5))-2*x^2-3)/x^2,x, algorithm="fricas")

[Out]

-(2*x^2 + 400*e^(e^5) - 3)/x

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giac [A]  time = 0.20, size = 16, normalized size = 0.59 \begin {gather*} -2 \, x - \frac {400 \, e^{\left (e^{5}\right )} - 3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((400*exp(exp(5))-2*x^2-3)/x^2,x, algorithm="giac")

[Out]

-2*x - (400*e^(e^5) - 3)/x

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maple [A]  time = 0.03, size = 17, normalized size = 0.63

method	result	size
default	\(-2 x -\frac {400 \,{\mathrm e}^{{\mathrm e}^{5}}-3}{x}\)	\(17\)
norman	\(\frac {-2 x^{2}+3-400 \,{\mathrm e}^{{\mathrm e}^{5}}}{x}\)	\(17\)
gosper	\(-\frac {2 x^{2}+400 \,{\mathrm e}^{{\mathrm e}^{5}}-3}{x}\)	\(18\)
risch	\(-2 x -\frac {400 \,{\mathrm e}^{{\mathrm e}^{5}}}{x}+\frac {3}{x}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((400*exp(exp(5))-2*x^2-3)/x^2,x,method=_RETURNVERBOSE)

[Out]

-2*x-(400*exp(exp(5))-3)/x

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maxima [A]  time = 0.36, size = 16, normalized size = 0.59 \begin {gather*} -2 \, x - \frac {400 \, e^{\left (e^{5}\right )} - 3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((400*exp(exp(5))-2*x^2-3)/x^2,x, algorithm="maxima")

[Out]

-2*x - (400*e^(e^5) - 3)/x

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mupad [B]  time = 0.05, size = 16, normalized size = 0.59 \begin {gather*} -2\,x-\frac {400\,{\mathrm {e}}^{{\mathrm {e}}^5}-3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x^2 - 400*exp(exp(5)) + 3)/x^2,x)

[Out]

- 2*x - (400*exp(exp(5)) - 3)/x

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sympy [A]  time = 0.10, size = 14, normalized size = 0.52 \begin {gather*} - 2 x - \frac {-3 + 400 e^{e^{5}}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((400*exp(exp(5))-2*x**2-3)/x**2,x)

[Out]

-2*x - (-3 + 400*exp(exp(5)))/x

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