3.47.9 \(\int \frac {1}{5} (-1-20 x^3-\log (x)) \, dx\)

Optimal. Leaf size=14 \[ 7-x^4-\frac {1}{5} x \log (x) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.93, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 2295} \begin {gather*} -x^4-\frac {1}{5} x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1 - 20*x^3 - Log[x])/5,x]

[Out]

-x^4 - (x*Log[x])/5

Rule 12

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

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (-1-20 x^3-\log (x)\right ) \, dx\\ &=-\frac {x}{5}-x^4-\frac {1}{5} \int \log (x) \, dx\\ &=-x^4-\frac {1}{5} x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} -x^4-\frac {1}{5} x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 - 20*x^3 - Log[x])/5,x]

[Out]

-x^4 - (x*Log[x])/5

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fricas [A]  time = 0.63, size = 11, normalized size = 0.79 \begin {gather*} -x^{4} - \frac {1}{5} \, x \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/5*log(x)-4*x^3-1/5,x, algorithm="fricas")

[Out]

-x^4 - 1/5*x*log(x)

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giac [A]  time = 0.14, size = 11, normalized size = 0.79 \begin {gather*} -x^{4} - \frac {1}{5} \, x \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/5*log(x)-4*x^3-1/5,x, algorithm="giac")

[Out]

-x^4 - 1/5*x*log(x)

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maple [A]  time = 0.01, size = 12, normalized size = 0.86

method	result	size
default	\(-x^{4}-\frac {x \ln \relax (x )}{5}\)	\(12\)
norman	\(-x^{4}-\frac {x \ln \relax (x )}{5}\)	\(12\)
risch	\(-x^{4}-\frac {x \ln \relax (x )}{5}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/5*ln(x)-4*x^3-1/5,x,method=_RETURNVERBOSE)

[Out]

-x^4-1/5*x*ln(x)

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maxima [A]  time = 0.37, size = 11, normalized size = 0.79 \begin {gather*} -x^{4} - \frac {1}{5} \, x \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/5*log(x)-4*x^3-1/5,x, algorithm="maxima")

[Out]

-x^4 - 1/5*x*log(x)

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mupad [B]  time = 3.15, size = 11, normalized size = 0.79 \begin {gather*} -\frac {x\,\ln \relax (x)}{5}-x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- log(x)/5 - 4*x^3 - 1/5,x)

[Out]

- (x*log(x))/5 - x^4

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sympy [A]  time = 0.08, size = 10, normalized size = 0.71 \begin {gather*} - x^{4} - \frac {x \log {\relax (x )}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/5*ln(x)-4*x**3-1/5,x)

[Out]

-x**4 - x*log(x)/5

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