3.20.95 \(\int \frac {3145728 e^{\frac {65536}{x^{48}}}-4 x^{49}}{x^{49}} \, dx\)

Optimal. Leaf size=13 \[ -e^{\frac {65536}{x^{48}}}-4 x \]

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Rubi [A]  time = 0.02, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {14, 2209} \begin {gather*} -e^{\frac {65536}{x^{48}}}-4 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3145728*E^(65536/x^48) - 4*x^49)/x^49,x]

[Out]

-E^(65536/x^48) - 4*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]]

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-4+\frac {3145728 e^{\frac {65536}{x^{48}}}}{x^{49}}\right ) \, dx\\ &=-4 x+3145728 \int \frac {e^{\frac {65536}{x^{48}}}}{x^{49}} \, dx\\ &=-e^{\frac {65536}{x^{48}}}-4 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} -e^{\frac {65536}{x^{48}}}-4 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3145728*E^(65536/x^48) - 4*x^49)/x^49,x]

[Out]

-E^(65536/x^48) - 4*x

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fricas [A]  time = 0.88, size = 12, normalized size = 0.92 \begin {gather*} -4 \, x - e^{\left (\frac {65536}{x^{48}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3145728*exp(65536/x^48)-4*x^49)/x^49,x, algorithm="fricas")

[Out]

-4*x - e^(65536/x^48)

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giac [A]  time = 0.17, size = 12, normalized size = 0.92 \begin {gather*} -4 \, x - e^{\left (\frac {65536}{x^{48}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3145728*exp(65536/x^48)-4*x^49)/x^49,x, algorithm="giac")

[Out]

-4*x - e^(65536/x^48)

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maple [A]  time = 0.04, size = 13, normalized size = 1.00

method	result	size
derivativedivides	\(-4 x -{\mathrm e}^{\frac {65536}{x^{48}}}\)	\(13\)
default	\(-4 x -{\mathrm e}^{\frac {65536}{x^{48}}}\)	\(13\)
risch	\(-4 x -{\mathrm e}^{\frac {65536}{x^{48}}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3145728*exp(65536/x^48)-4*x^49)/x^49,x,method=_RETURNVERBOSE)

[Out]

-4*x-exp(1/x^48)^65536

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maxima [A]  time = 0.45, size = 12, normalized size = 0.92 \begin {gather*} -4 \, x - e^{\left (\frac {65536}{x^{48}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3145728*exp(65536/x^48)-4*x^49)/x^49,x, algorithm="maxima")

[Out]

-4*x - e^(65536/x^48)

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mupad [B]  time = 1.19, size = 12, normalized size = 0.92 \begin {gather*} -4\,x-{\mathrm {e}}^{\frac {65536}{x^{48}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3145728*exp(65536/x^48) - 4*x^49)/x^49,x)

[Out]

- 4*x - exp(65536/x^48)

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sympy [A]  time = 0.10, size = 10, normalized size = 0.77 \begin {gather*} - 4 x - e^{\frac {65536}{x^{48}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3145728*exp(65536/x**48)-4*x**49)/x**49,x)

[Out]

-4*x - exp(65536/x**48)

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