3.85.24 \(\int \frac {1+10 x-380 x^2+93 x^3-2944 x^4-1280 x^5}{x} \, dx\)

Optimal. Leaf size=24 \[ -x+(3+x) \left (x-\left (-2+x-16 x^2\right )^2\right )+\log (x) \]

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Rubi [A]  time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.08, number of steps used = 2, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {14} \begin {gather*} -256 x^5-736 x^4+31 x^3-190 x^2+10 x+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 + 10*x - 380*x^2 + 93*x^3 - 2944*x^4 - 1280*x^5)/x,x]

[Out]

10*x - 190*x^2 + 31*x^3 - 736*x^4 - 256*x^5 + 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 (10+\frac {1}{x}-380 x+93 x^2-2944 x^3-1280 x^4\right ) \, dx\\ &=10 x-190 x^2+31 x^3-736 x^4-256 x^5+\log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 26, normalized size = 1.08 \begin {gather*} 10 x-190 x^2+31 x^3-736 x^4-256 x^5+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + 10*x - 380*x^2 + 93*x^3 - 2944*x^4 - 1280*x^5)/x,x]

[Out]

10*x - 190*x^2 + 31*x^3 - 736*x^4 - 256*x^5 + Log[x]

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fricas [A]  time = 1.05, size = 26, normalized size = 1.08 \begin {gather*} -256 \, x^{5} - 736 \, x^{4} + 31 \, x^{3} - 190 \, x^{2} + 10 \, x + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1280*x^5-2944*x^4+93*x^3-380*x^2+10*x+1)/x,x, algorithm="fricas")

[Out]

-256*x^5 - 736*x^4 + 31*x^3 - 190*x^2 + 10*x + log(x)

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giac [A]  time = 0.11, size = 27, normalized size = 1.12 \begin {gather*} -256 \, x^{5} - 736 \, x^{4} + 31 \, x^{3} - 190 \, x^{2} + 10 \, x + \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1280*x^5-2944*x^4+93*x^3-380*x^2+10*x+1)/x,x, algorithm="giac")

[Out]

-256*x^5 - 736*x^4 + 31*x^3 - 190*x^2 + 10*x + log(abs(x))

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maple [A]  time = 0.02, size = 27, normalized size = 1.12

method	result	size
default	\(-256 x^{5}-736 x^{4}+31 x^{3}-190 x^{2}+10 x +\ln \relax (x )\)	\(27\)
norman	\(-256 x^{5}-736 x^{4}+31 x^{3}-190 x^{2}+10 x +\ln \relax (x )\)	\(27\)
risch	\(-256 x^{5}-736 x^{4}+31 x^{3}-190 x^{2}+10 x +\ln \relax (x )\)	\(27\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-1280*x^5-2944*x^4+93*x^3-380*x^2+10*x+1)/x,x,method=_RETURNVERBOSE)

[Out]

-256*x^5-736*x^4+31*x^3-190*x^2+10*x+ln(x)

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maxima [A]  time = 0.59, size = 26, normalized size = 1.08 \begin {gather*} -256 \, x^{5} - 736 \, x^{4} + 31 \, x^{3} - 190 \, x^{2} + 10 \, x + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1280*x^5-2944*x^4+93*x^3-380*x^2+10*x+1)/x,x, algorithm="maxima")

[Out]

-256*x^5 - 736*x^4 + 31*x^3 - 190*x^2 + 10*x + log(x)

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mupad [B]  time = 0.03, size = 26, normalized size = 1.08 \begin {gather*} 10\,x+\ln \relax (x)-190\,x^2+31\,x^3-736\,x^4-256\,x^5 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*x - 380*x^2 + 93*x^3 - 2944*x^4 - 1280*x^5 + 1)/x,x)

[Out]

10*x + log(x) - 190*x^2 + 31*x^3 - 736*x^4 - 256*x^5

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sympy [A]  time = 0.08, size = 26, normalized size = 1.08 \begin {gather*} - 256 x^{5} - 736 x^{4} + 31 x^{3} - 190 x^{2} + 10 x + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-1280*x**5-2944*x**4+93*x**3-380*x**2+10*x+1)/x,x)

[Out]

-256*x**5 - 736*x**4 + 31*x**3 - 190*x**2 + 10*x + log(x)

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