3.28.14 \(\int \frac {15}{4 x^2} \, dx\)

Optimal. Leaf size=23 \[ \log \left (e^{-\frac {15+e^{-e^{5+e}} x}{4 x}}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.30, 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} \begin {gather*} -\frac {15}{4 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[15/(4*x^2),x]

[Out]

-15/(4*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} &=\frac {15}{4} \int \frac {1}{x^2} \, dx\\ &=-\frac {15}{4 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.30 \begin {gather*} -\frac {15}{4 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[15/(4*x^2),x]

[Out]

-15/(4*x)

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fricas [A]  time = 0.50, size = 5, normalized size = 0.22 \begin {gather*} -\frac {15}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(15/4/x^2,x, algorithm="fricas")

[Out]

-15/4/x

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giac [A]  time = 0.42, size = 5, normalized size = 0.22 \begin {gather*} -\frac {15}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(15/4/x^2,x, algorithm="giac")

[Out]

-15/4/x

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maple [A]  time = 0.01, size = 6, normalized size = 0.26

method	result	size
gosper	\(-\frac {15}{4 x}\)	\(6\)
default	\(-\frac {15}{4 x}\)	\(6\)
norman	\(-\frac {15}{4 x}\)	\(6\)
risch	\(-\frac {15}{4 x}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(15/4/x^2,x,method=_RETURNVERBOSE)

[Out]

-15/4/x

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maxima [A]  time = 0.47, size = 5, normalized size = 0.22 \begin {gather*} -\frac {15}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(15/4/x^2,x, algorithm="maxima")

[Out]

-15/4/x

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mupad [B]  time = 0.02, size = 5, normalized size = 0.22 \begin {gather*} -\frac {15}{4\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(15/(4*x^2),x)

[Out]

-15/(4*x)

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sympy [A]  time = 0.06, size = 5, normalized size = 0.22 \begin {gather*} - \frac {15}{4 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(15/4/x**2,x)

[Out]

-15/(4*x)

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