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

Optimal. Leaf size=14 \[ \frac {-16+\frac {8 x}{9 e^3}}{x} \]

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.36, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \begin {gather*} -\frac {16}{x} \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=16 \int \frac {1}{x^2} \, dx\\ &=-\frac {16}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 5, normalized size = 0.36 \begin {gather*} -\frac {16}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[16/x^2,x]

[Out]

-16/x

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Maple [A]
time = 0.01, size = 6, normalized size = 0.43

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-16/x

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Maxima [A]
time = 0.25, size = 5, normalized size = 0.36 \begin {gather*} -\frac {16}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-16/x

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Fricas [A]
time = 0.40, size = 5, normalized size = 0.36 \begin {gather*} -\frac {16}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-16/x

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Sympy [A]
time = 0.01, size = 3, normalized size = 0.21 \begin {gather*} - \frac {16}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16/x**2,x)

[Out]

-16/x

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Giac [A]
time = 0.40, size = 5, normalized size = 0.36 \begin {gather*} -\frac {16}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16/x^2,x, algorithm="giac")

[Out]

-16/x

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Mupad [B]
time = 0.01, size = 5, normalized size = 0.36 \begin {gather*} -\frac {16}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(16/x^2,x)

[Out]

-16/x

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