\(\int \frac {1-3 x^3}{x} \, dx\) [4193]

Optimal result

Integrand size = 11, antiderivative size = 15 \[ \int \frac {1-3 x^3}{x} \, dx=e^{e^4}-x^3+\log (-2 x) \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ \int \frac {1-3 x^3}{x} \, dx=\log (x)-x^3 \]

[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{align*} \text {integral}& = \int \left (\frac {1}{x}-3 x^2\right ) \, dx \\ & = -x^3+\log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {1-3 x^3}{x} \, dx=-x^3+\log (x) \]

[In]

Integrate[(1 - 3*x^3)/x,x]

[Out]

-x^3 + Log[x]

Maple [A] (verified)

Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60

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

[In]

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

[Out]

-x^3+ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {1-3 x^3}{x} \, dx=-x^{3} + \log \left (x\right ) \]

[In]

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

[Out]

-x^3 + log(x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33 \[ \int \frac {1-3 x^3}{x} \, dx=- x^{3} + \log {\left (x \right )} \]

[In]

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

[Out]

-x**3 + log(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {1-3 x^3}{x} \, dx=-x^{3} + \frac {1}{3} \, \log \left (x^{3}\right ) \]

[In]

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

[Out]

-x^3 + 1/3*log(x^3)

Giac [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int \frac {1-3 x^3}{x} \, dx=-x^{3} + \log \left ({\left | x \right |}\right ) \]

[In]

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

[Out]

-x^3 + log(abs(x))

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {1-3 x^3}{x} \, dx=\ln \left (x\right )-x^3 \]

[In]

int(-(3*x^3 - 1)/x,x)

[Out]

log(x) - x^3