\(\int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx\) [7831]

Optimal result

Integrand size = 19, antiderivative size = 20 \[ \int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx=9 \left (x-(3-x) x-256 x^4\right )+\log (x) \]

[Out]

9*x-9*x*(-x+3)-2304*x^4+ln(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {14} \[ \int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx=-2304 x^4+9 x^2-18 x+\log (x) \]

[In]

Int[(1 - 18*x + 18*x^2 - 9216*x^4)/x,x]

[Out]

-18*x + 9*x^2 - 2304*x^4 + 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 (-18+\frac {1}{x}+18 x-9216 x^3\right ) \, dx \\ & = -18 x+9 x^2-2304 x^4+\log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx=-18 x+9 x^2-2304 x^4+\log (x) \]

[In]

Integrate[(1 - 18*x + 18*x^2 - 9216*x^4)/x,x]

[Out]

-18*x + 9*x^2 - 2304*x^4 + Log[x]

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85

method	result	size
default	\(-2304 x^{4}+9 x^{2}-18 x +\ln \left (x \right )\)	\(17\)
norman	\(-2304 x^{4}+9 x^{2}-18 x +\ln \left (x \right )\)	\(17\)
risch	\(-2304 x^{4}+9 x^{2}-18 x +\ln \left (x \right )\)	\(17\)
parallelrisch	\(-2304 x^{4}+9 x^{2}-18 x +\ln \left (x \right )\)	\(17\)

[In]

int((-9216*x^4+18*x^2-18*x+1)/x,x,method=_RETURNVERBOSE)

[Out]

-2304*x^4+9*x^2-18*x+ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx=-2304 \, x^{4} + 9 \, x^{2} - 18 \, x + \log \left (x\right ) \]

[In]

integrate((-9216*x^4+18*x^2-18*x+1)/x,x, algorithm="fricas")

[Out]

-2304*x^4 + 9*x^2 - 18*x + log(x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx=- 2304 x^{4} + 9 x^{2} - 18 x + \log {\left (x \right )} \]

[In]

integrate((-9216*x**4+18*x**2-18*x+1)/x,x)

[Out]

-2304*x**4 + 9*x**2 - 18*x + log(x)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx=-2304 \, x^{4} + 9 \, x^{2} - 18 \, x + \log \left (x\right ) \]

[In]

integrate((-9216*x^4+18*x^2-18*x+1)/x,x, algorithm="maxima")

[Out]

-2304*x^4 + 9*x^2 - 18*x + log(x)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx=-2304 \, x^{4} + 9 \, x^{2} - 18 \, x + \log \left ({\left | x \right |}\right ) \]

[In]

integrate((-9216*x^4+18*x^2-18*x+1)/x,x, algorithm="giac")

[Out]

-2304*x^4 + 9*x^2 - 18*x + log(abs(x))

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1-18 x+18 x^2-9216 x^4}{x} \, dx=\ln \left (x\right )-18\,x+9\,x^2-2304\,x^4 \]

[In]

int(-(18*x - 18*x^2 + 9216*x^4 - 1)/x,x)

[Out]

log(x) - 18*x + 9*x^2 - 2304*x^4