3.22.86 \(\int \frac {200-40 e^{32}+2 e^{64}-2 x^4}{x^3} \, dx\)

Optimal. Leaf size=21 \[ 3-\left (\frac {10-e^{32}}{x}-x\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 20, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {14} \begin {gather*} -x^2-\frac {\left (10-e^{32}\right )^2}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(200 - 40*E^32 + 2*E^64 - 2*x^4)/x^3,x]

[Out]

-((10 - E^32)^2/x^2) - x^2

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 (\frac {2 \left (-10+e^{32}\right )^2}{x^3}-2 x\right ) \, dx\\ &=-\frac {\left (10-e^{32}\right )^2}{x^2}-x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 18, normalized size = 0.86 \begin {gather*} -\frac {100-20 e^{32}+e^{64}+x^4}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(200 - 40*E^32 + 2*E^64 - 2*x^4)/x^3,x]

[Out]

-((100 - 20*E^32 + E^64 + x^4)/x^2)

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fricas [A]  time = 1.39, size = 16, normalized size = 0.76 \begin {gather*} -\frac {x^{4} + e^{64} - 20 \, e^{32} + 100}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(16)^4-40*exp(16)^2-2*x^4+200)/x^3,x, algorithm="fricas")

[Out]

-(x^4 + e^64 - 20*e^32 + 100)/x^2

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giac [A]  time = 0.29, size = 19, normalized size = 0.90 \begin {gather*} -x^{2} - \frac {e^{64} - 20 \, e^{32} + 100}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(16)^4-40*exp(16)^2-2*x^4+200)/x^3,x, algorithm="giac")

[Out]

-x^2 - (e^64 - 20*e^32 + 100)/x^2

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maple [A]  time = 0.05, size = 20, normalized size = 0.95

method	result	size
default	\(-x^{2}-\frac {{\mathrm e}^{64}-20 \,{\mathrm e}^{32}+100}{x^{2}}\)	\(20\)
gosper	\(-\frac {{\mathrm e}^{64}+x^{4}-20 \,{\mathrm e}^{32}+100}{x^{2}}\)	\(21\)
norman	\(\frac {-{\mathrm e}^{64}-x^{4}+20 \,{\mathrm e}^{32}-100}{x^{2}}\)	\(24\)
risch	\(-x^{2}-\frac {{\mathrm e}^{64}}{x^{2}}+\frac {20 \,{\mathrm e}^{32}}{x^{2}}-\frac {100}{x^{2}}\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(16)^4-40*exp(16)^2-2*x^4+200)/x^3,x,method=_RETURNVERBOSE)

[Out]

-x^2-(exp(64)-20*exp(32)+100)/x^2

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maxima [A]  time = 0.52, size = 19, normalized size = 0.90 \begin {gather*} -x^{2} - \frac {e^{64} - 20 \, e^{32} + 100}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(16)^4-40*exp(16)^2-2*x^4+200)/x^3,x, algorithm="maxima")

[Out]

-x^2 - (e^64 - 20*e^32 + 100)/x^2

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mupad [B]  time = 0.05, size = 17, normalized size = 0.81 \begin {gather*} -\frac {{\left ({\mathrm {e}}^{32}-10\right )}^2}{x^2}-x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(40*exp(32) - 2*exp(64) + 2*x^4 - 200)/x^3,x)

[Out]

- (exp(32) - 10)^2/x^2 - x^2

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sympy [A]  time = 0.12, size = 17, normalized size = 0.81 \begin {gather*} - x^{2} - \frac {- 20 e^{32} + 100 + e^{64}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(16)**4-40*exp(16)**2-2*x**4+200)/x**3,x)

[Out]

-x**2 - (-20*exp(32) + 100 + exp(64))/x**2

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