3.23 \(\int \frac {1}{d x^3} \, dx\)

Optimal. Leaf size=10 \[ -\frac {1}{2 d x^2} \]

[Out]

-1/2/d/x^2

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 30} \[ -\frac {1}{2 d x^2} \]

Antiderivative was successfully verified.

[In]

Int[1/(d*x^3),x]

[Out]

-1/(2*d*x^2)

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*} \int \frac {1}{d x^3} \, dx &=\frac {\int \frac {1}{x^3} \, dx}{d}\\ &=-\frac {1}{2 d x^2}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \[ -\frac {1}{2 d x^2} \]

Antiderivative was successfully verified.

[In]

Integrate[1/(d*x^3),x]

[Out]

-1/2*1/(d*x^2)

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fricas [A]  time = 0.70, size = 8, normalized size = 0.80 \[ -\frac {1}{2 \, d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/d/x^3,x, algorithm="fricas")

[Out]

-1/2/(d*x^2)

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giac [A]  time = 0.27, size = 8, normalized size = 0.80 \[ -\frac {1}{2 \, d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/d/x^3,x, algorithm="giac")

[Out]

-1/2/(d*x^2)

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maple [A]  time = 0.00, size = 9, normalized size = 0.90 \[ -\frac {1}{2 d \,x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/d/x^3,x)

[Out]

-1/2/d/x^2

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maxima [A]  time = 0.63, size = 8, normalized size = 0.80 \[ -\frac {1}{2 \, d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/d/x^3,x, algorithm="maxima")

[Out]

-1/2/(d*x^2)

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mupad [B]  time = 0.03, size = 8, normalized size = 0.80 \[ -\frac {1}{2\,d\,x^2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(d*x^3),x)

[Out]

-1/(2*d*x^2)

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sympy [A]  time = 0.06, size = 8, normalized size = 0.80 \[ - \frac {1}{2 d x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/d/x**3,x)

[Out]

-1/(2*d*x**2)

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