3.86.42 \(\int \frac {-3-8 x^2}{x} \, dx\)

Optimal. Leaf size=15 \[ 1-4 x^2-\log \left (3125 x^3\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \begin {gather*} -4 x^2-3 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-3 - 8*x^2)/x,x]

[Out]

-4*x^2 - 3*Log[x]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {3}{x}-8 x\right ) \, dx\\ &=-4 x^2-3 \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.67 \begin {gather*} -4 x^2-3 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3 - 8*x^2)/x,x]

[Out]

-4*x^2 - 3*Log[x]

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fricas [A]  time = 0.60, size = 10, normalized size = 0.67 \begin {gather*} -4 \, x^{2} - 3 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x^2-3)/x,x, algorithm="fricas")

[Out]

-4*x^2 - 3*log(x)

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giac [A]  time = 0.17, size = 12, normalized size = 0.80 \begin {gather*} -4 \, x^{2} - \frac {3}{2} \, \log \left (x^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x^2-3)/x,x, algorithm="giac")

[Out]

-4*x^2 - 3/2*log(x^2)

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maple [A]  time = 0.02, size = 11, normalized size = 0.73

method	result	size
default	\(-4 x^{2}-3 \ln \relax (x )\)	\(11\)
norman	\(-4 x^{2}-3 \ln \relax (x )\)	\(11\)
risch	\(-4 x^{2}-3 \ln \relax (x )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-8*x^2-3)/x,x,method=_RETURNVERBOSE)

[Out]

-4*x^2-3*ln(x)

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maxima [A]  time = 0.35, size = 12, normalized size = 0.80 \begin {gather*} -4 \, x^{2} - \frac {3}{2} \, \log \left (x^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x^2-3)/x,x, algorithm="maxima")

[Out]

-4*x^2 - 3/2*log(x^2)

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mupad [B]  time = 0.02, size = 10, normalized size = 0.67 \begin {gather*} -3\,\ln \relax (x)-4\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(8*x^2 + 3)/x,x)

[Out]

- 3*log(x) - 4*x^2

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sympy [A]  time = 0.07, size = 10, normalized size = 0.67 \begin {gather*} - 4 x^{2} - 3 \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x**2-3)/x,x)

[Out]

-4*x**2 - 3*log(x)

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