3.42.93 \(\int \frac {1-3 x^3}{x} \, dx\)

Optimal. Leaf size=15 \[ e^{e^4}-x^3+\log (-2 x) \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.53, 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*} \log (x)-x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 3*x^3)/x,x]

[Out]

-x^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 {1}{x}-3 x^2\right ) \, dx\\ &=-x^3+\log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.53 \begin {gather*} -x^3+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 3*x^3)/x,x]

[Out]

-x^3 + Log[x]

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fricas [A]  time = 1.26, size = 8, normalized size = 0.53 \begin {gather*} -x^{3} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^3+1)/x,x, algorithm="fricas")

[Out]

-x^3 + log(x)

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giac [A]  time = 0.25, size = 9, normalized size = 0.60 \begin {gather*} -x^{3} + \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^3+1)/x,x, algorithm="giac")

[Out]

-x^3 + log(abs(x))

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maple [A]  time = 0.01, size = 9, normalized size = 0.60

method	result	size
default	\(-x^{3}+\ln \relax (x )\)	\(9\)
norman	\(-x^{3}+\ln \relax (x )\)	\(9\)
risch	\(-x^{3}+\ln \relax (x )\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-3*x^3+1)/x,x,method=_RETURNVERBOSE)

[Out]

-x^3+ln(x)

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maxima [A]  time = 0.35, size = 12, normalized size = 0.80 \begin {gather*} -x^{3} + \frac {1}{3} \, \log \left (x^{3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^3+1)/x,x, algorithm="maxima")

[Out]

-x^3 + 1/3*log(x^3)

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mupad [B]  time = 0.03, size = 8, normalized size = 0.53 \begin {gather*} \ln \relax (x)-x^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*x^3 - 1)/x,x)

[Out]

log(x) - x^3

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sympy [A]  time = 0.07, size = 5, normalized size = 0.33 \begin {gather*} - x^{3} + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x**3+1)/x,x)

[Out]

-x**3 + log(x)

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