3.70.10 \(\int \frac {1-e^{16}}{x^2} \, dx\)

Optimal. Leaf size=9 \[ \frac {-1+e^{16}}{x} \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.33, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 30} \begin {gather*} -\frac {1-e^{16}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - E^16)/x^2,x]

[Out]

-((1 - E^16)/x)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (1-e^{16}\right ) \int \frac {1}{x^2} \, dx\\ &=-\frac {1-e^{16}}{x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 12, normalized size = 1.33 \begin {gather*} -\frac {1-e^{16}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - E^16)/x^2,x]

[Out]

-((1 - E^16)/x)

________________________________________________________________________________________

fricas [A]  time = 0.52, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{16} - 1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(16)+1)/x^2,x, algorithm="fricas")

[Out]

(e^16 - 1)/x

________________________________________________________________________________________

giac [A]  time = 0.22, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{16} - 1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(16)+1)/x^2,x, algorithm="giac")

[Out]

(e^16 - 1)/x

________________________________________________________________________________________

maple [A]  time = 0.02, size = 9, normalized size = 1.00

method	result	size
gosper	\(\frac {-1+{\mathrm e}^{16}}{x}\)	\(9\)
norman	\(\frac {-1+{\mathrm e}^{16}}{x}\)	\(9\)
default	\(-\frac {-{\mathrm e}^{16}+1}{x}\)	\(12\)
risch	\(\frac {{\mathrm e}^{16}}{x}-\frac {1}{x}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-exp(16)+1)/x^2,x,method=_RETURNVERBOSE)

[Out]

(-1+exp(16))/x

________________________________________________________________________________________

maxima [A]  time = 0.37, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{16} - 1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(16)+1)/x^2,x, algorithm="maxima")

[Out]

(e^16 - 1)/x

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 8, normalized size = 0.89 \begin {gather*} \frac {{\mathrm {e}}^{16}-1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(16) - 1)/x^2,x)

[Out]

(exp(16) - 1)/x

________________________________________________________________________________________

sympy [A]  time = 0.06, size = 7, normalized size = 0.78 \begin {gather*} - \frac {1 - e^{16}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(16)+1)/x**2,x)

[Out]

-(1 - exp(16))/x

________________________________________________________________________________________