3.101.8 \(\int \frac {-1-80 x^8}{10 x} \, dx\)

Optimal. Leaf size=13 \[ 1-x^8-\frac {\log (x)}{10} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14} \begin {gather*} -x^8-\frac {\log (x)}{10} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1 - 80*x^8)/(10*x),x]

[Out]

-x^8 - Log[x]/10

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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} &=\frac {1}{10} \int \frac {-1-80 x^8}{x} \, dx\\ &=\frac {1}{10} \int \left (-\frac {1}{x}-80 x^7\right ) \, dx\\ &=-x^8-\frac {\log (x)}{10}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.92 \begin {gather*} -x^8-\frac {\log (x)}{10} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 - 80*x^8)/(10*x),x]

[Out]

-x^8 - Log[x]/10

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fricas [A]  time = 0.70, size = 10, normalized size = 0.77 \begin {gather*} -x^{8} - \frac {1}{10} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/10*(-80*x^8-1)/x,x, algorithm="fricas")

[Out]

-x^8 - 1/10*log(x)

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giac [A]  time = 0.13, size = 12, normalized size = 0.92 \begin {gather*} -x^{8} - \frac {1}{80} \, \log \left (x^{8}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/10*(-80*x^8-1)/x,x, algorithm="giac")

[Out]

-x^8 - 1/80*log(x^8)

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maple [A]  time = 0.02, size = 11, normalized size = 0.85

method	result	size
default	\(-x^{8}-\frac {\ln \relax (x )}{10}\)	\(11\)
norman	\(-x^{8}-\frac {\ln \relax (x )}{10}\)	\(11\)
risch	\(-x^{8}-\frac {\ln \relax (x )}{10}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/10*(-80*x^8-1)/x,x,method=_RETURNVERBOSE)

[Out]

-x^8-1/10*ln(x)

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maxima [A]  time = 0.39, size = 12, normalized size = 0.92 \begin {gather*} -x^{8} - \frac {1}{80} \, \log \left (x^{8}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/10*(-80*x^8-1)/x,x, algorithm="maxima")

[Out]

-x^8 - 1/80*log(x^8)

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mupad [B]  time = 6.16, size = 10, normalized size = 0.77 \begin {gather*} -\frac {\ln \relax (x)}{10}-x^8 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(8*x^8 + 1/10)/x,x)

[Out]

- log(x)/10 - x^8

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sympy [A]  time = 0.07, size = 8, normalized size = 0.62 \begin {gather*} - x^{8} - \frac {\log {\relax (x )}}{10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/10*(-80*x**8-1)/x,x)

[Out]

-x**8 - log(x)/10

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