3.97.14 \(\int \frac {9-27 \log (x)}{40 x^4} \, dx\)

Optimal. Leaf size=9 \[ \frac {9 \log (x)}{40 x^3} \]

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Rubi [A]  time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2303} \begin {gather*} \frac {9 \log (x)}{40 x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(9 - 27*Log[x])/(40*x^4),x]

[Out]

(9*Log[x])/(40*x^3)

Rule 12

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

Rule 2303

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(b*(d*x)^(m + 1)*Log[c*x^n])/(
d*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1] && EqQ[a*(m + 1) - b*n, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{40} \int \frac {9-27 \log (x)}{x^4} \, dx\\ &=\frac {9 \log (x)}{40 x^3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {9 \log (x)}{40 x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(9 - 27*Log[x])/(40*x^4),x]

[Out]

(9*Log[x])/(40*x^3)

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fricas [A]  time = 0.54, size = 7, normalized size = 0.78 \begin {gather*} \frac {9 \, \log \relax (x)}{40 \, x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/40*(-27*log(x)+9)/x^4,x, algorithm="fricas")

[Out]

9/40*log(x)/x^3

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giac [A]  time = 0.14, size = 7, normalized size = 0.78 \begin {gather*} \frac {9 \, \log \relax (x)}{40 \, x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/40*(-27*log(x)+9)/x^4,x, algorithm="giac")

[Out]

9/40*log(x)/x^3

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maple [A]  time = 0.02, size = 8, normalized size = 0.89

method	result	size
default	\(\frac {9 \ln \relax (x )}{40 x^{3}}\)	\(8\)
norman	\(\frac {9 \ln \relax (x )}{40 x^{3}}\)	\(8\)
risch	\(\frac {9 \ln \relax (x )}{40 x^{3}}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/40*(-27*ln(x)+9)/x^4,x,method=_RETURNVERBOSE)

[Out]

9/40*ln(x)/x^3

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maxima [B]  time = 0.36, size = 17, normalized size = 1.89 \begin {gather*} \frac {3 \, {\left (3 \, \log \relax (x) + 1\right )}}{40 \, x^{3}} - \frac {3}{40 \, x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/40*(-27*log(x)+9)/x^4,x, algorithm="maxima")

[Out]

3/40*(3*log(x) + 1)/x^3 - 3/40/x^3

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mupad [B]  time = 5.82, size = 7, normalized size = 0.78 \begin {gather*} \frac {9\,\ln \relax (x)}{40\,x^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((27*log(x))/40 - 9/40)/x^4,x)

[Out]

(9*log(x))/(40*x^3)

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sympy [A]  time = 0.09, size = 8, normalized size = 0.89 \begin {gather*} \frac {9 \log {\relax (x )}}{40 x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/40*(-27*ln(x)+9)/x**4,x)

[Out]

9*log(x)/(40*x**3)

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