3.15.100 \(\int \frac {-1-25 x+18 x^2-3 x^3}{x} \, dx\)

Optimal. Leaf size=19 \[ 6-x \left ((-5+x)^2+x\right )-\log (x \log (5)) \]

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Rubi [A]  time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {14} \begin {gather*} -x^3+9 x^2-25 x-\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1 - 25*x + 18*x^2 - 3*x^3)/x,x]

[Out]

-25*x + 9*x^2 - 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 (-25-\frac {1}{x}+18 x-3 x^2\right ) \, dx\\ &=-25 x+9 x^2-x^3-\log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 18, normalized size = 0.95 \begin {gather*} -25 x+9 x^2-x^3-\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 - 25*x + 18*x^2 - 3*x^3)/x,x]

[Out]

-25*x + 9*x^2 - x^3 - Log[x]

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fricas [A]  time = 0.66, size = 18, normalized size = 0.95 \begin {gather*} -x^{3} + 9 \, x^{2} - 25 \, x - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^3+18*x^2-25*x-1)/x,x, algorithm="fricas")

[Out]

-x^3 + 9*x^2 - 25*x - log(x)

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giac [A]  time = 0.17, size = 19, normalized size = 1.00 \begin {gather*} -x^{3} + 9 \, x^{2} - 25 \, x - \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^3+18*x^2-25*x-1)/x,x, algorithm="giac")

[Out]

-x^3 + 9*x^2 - 25*x - log(abs(x))

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maple [A]  time = 0.02, size = 19, normalized size = 1.00

method	result	size
default	\(-x^{3}+9 x^{2}-25 x -\ln \relax (x )\)	\(19\)
norman	\(-x^{3}+9 x^{2}-25 x -\ln \relax (x )\)	\(19\)
risch	\(-x^{3}+9 x^{2}-25 x -\ln \relax (x )\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-3*x^3+18*x^2-25*x-1)/x,x,method=_RETURNVERBOSE)

[Out]

-x^3+9*x^2-25*x-ln(x)

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maxima [A]  time = 0.49, size = 18, normalized size = 0.95 \begin {gather*} -x^{3} + 9 \, x^{2} - 25 \, x - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x^3+18*x^2-25*x-1)/x,x, algorithm="maxima")

[Out]

-x^3 + 9*x^2 - 25*x - log(x)

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mupad [B]  time = 0.03, size = 18, normalized size = 0.95 \begin {gather*} 9\,x^2-\ln \relax (x)-25\,x-x^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(25*x - 18*x^2 + 3*x^3 + 1)/x,x)

[Out]

9*x^2 - log(x) - 25*x - x^3

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sympy [A]  time = 0.07, size = 14, normalized size = 0.74 \begin {gather*} - x^{3} + 9 x^{2} - 25 x - \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x**3+18*x**2-25*x-1)/x,x)

[Out]

-x**3 + 9*x**2 - 25*x - log(x)

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