\(\int \frac {16}{x^2} \, dx\) [10012]

Optimal result

Integrand size = 5, antiderivative size = 14 \[ \int \frac {16}{x^2} \, dx=\frac {-16+\frac {8 x}{9 e^3}}{x} \]

[Out]

1/x*(-16+8/9*x/exp(3))

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \[ \int \frac {16}{x^2} \, dx=-\frac {16}{x} \]

[In]

Int[16/x^2,x]

[Out]

-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{align*} \text {integral}& = 16 \int \frac {1}{x^2} \, dx \\ & = -\frac {16}{x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36 \[ \int \frac {16}{x^2} \, dx=-\frac {16}{x} \]

[In]

Integrate[16/x^2,x]

[Out]

-16/x

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.43

method	result	size
gosper	\(-\frac {16}{x}\)	\(6\)
default	\(-\frac {16}{x}\)	\(6\)
norman	\(-\frac {16}{x}\)	\(6\)
risch	\(-\frac {16}{x}\)	\(6\)
parallelrisch	\(-\frac {16}{x}\)	\(6\)

[In]

int(16/x^2,x,method=_RETURNVERBOSE)

[Out]

-16/x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36 \[ \int \frac {16}{x^2} \, dx=-\frac {16}{x} \]

[In]

integrate(16/x^2,x, algorithm="fricas")

[Out]

-16/x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.21 \[ \int \frac {16}{x^2} \, dx=- \frac {16}{x} \]

[In]

integrate(16/x**2,x)

[Out]

-16/x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36 \[ \int \frac {16}{x^2} \, dx=-\frac {16}{x} \]

[In]

integrate(16/x^2,x, algorithm="maxima")

[Out]

-16/x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36 \[ \int \frac {16}{x^2} \, dx=-\frac {16}{x} \]

[In]

integrate(16/x^2,x, algorithm="giac")

[Out]

-16/x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36 \[ \int \frac {16}{x^2} \, dx=-\frac {16}{x} \]

[In]

int(16/x^2,x)

[Out]

-16/x