3.86.52 \(\int \frac {e^{16}+x^2}{x^2} \, dx\)

Optimal. Leaf size=17 \[ 10+e-\frac {e^{16}-x^2}{x} \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.59, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \begin {gather*} x-\frac {e^{16}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^16 + x^2)/x^2,x]

[Out]

-(E^16/x) + 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 (1+\frac {e^{16}}{x^2}\right ) \, dx\\ &=-\frac {e^{16}}{x}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.59 \begin {gather*} -\frac {e^{16}}{x}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^16 + x^2)/x^2,x]

[Out]

-(E^16/x) + x

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fricas [A]  time = 0.51, size = 12, normalized size = 0.71 \begin {gather*} \frac {x^{2} - e^{16}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(4)^4+x^2)/x^2,x, algorithm="fricas")

[Out]

(x^2 - e^16)/x

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giac [A]  time = 0.14, size = 9, normalized size = 0.53 \begin {gather*} x - \frac {e^{16}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(4)^4+x^2)/x^2,x, algorithm="giac")

[Out]

x - e^16/x

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maple [A]  time = 0.03, size = 10, normalized size = 0.59

method	result	size
default	\(x -\frac {{\mathrm e}^{16}}{x}\)	\(10\)
risch	\(x -\frac {{\mathrm e}^{16}}{x}\)	\(10\)
norman	\(\frac {x^{2}-{\mathrm e}^{16}}{x}\)	\(15\)
gosper	\(-\frac {{\mathrm e}^{16}-x^{2}}{x}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(4)^4+x^2)/x^2,x,method=_RETURNVERBOSE)

[Out]

x-exp(16)/x

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maxima [A]  time = 0.36, size = 9, normalized size = 0.53 \begin {gather*} x - \frac {e^{16}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(4)^4+x^2)/x^2,x, algorithm="maxima")

[Out]

x - e^16/x

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mupad [B]  time = 5.15, size = 9, normalized size = 0.53 \begin {gather*} x-\frac {{\mathrm {e}}^{16}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(16) + x^2)/x^2,x)

[Out]

x - exp(16)/x

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sympy [A]  time = 0.07, size = 5, normalized size = 0.29 \begin {gather*} x - \frac {e^{16}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(4)**4+x**2)/x**2,x)

[Out]

x - exp(16)/x

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