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

Optimal. Leaf size=24 $$-x+(3+x)(x-{(-2+x-16x^2)}^2)+\log (x)$$

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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} $$\begin{array}{c}-256x^5-736x^4+31x^3-190x^2+10x+\log (x)\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (10+\frac{1}{x}-380x+93x^2-2944x^3-1280x^4)dx\\ & =10x-190x^2+31x^3-736x^4-256x^5+\log (x)\end{array}\end{array}$$

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

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 $$\begin{array}{c}-256x^5-736x^4+31x^3-190x^2+10x+\log (x)\end{array}$$

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 $$\begin{array}{c}-256x^5-736x^4+31x^3-190x^2+10x+\log \left(\left|x\right|\right)\end{array}$$

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	$-256x^5-736x^4+31x^3-190x^2+10x+\ln (x)$	$27$
norman	$-256x^5-736x^4+31x^3-190x^2+10x+\ln (x)$	$27$
risch	$-256x^5-736x^4+31x^3-190x^2+10x+\ln (x)$	$27$

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 $$\begin{array}{c}-256x^5-736x^4+31x^3-190x^2+10x+\log (x)\end{array}$$

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 $$\begin{array}{c}10x+\ln (x)-190x^2+31x^3-736x^4-256x^5\end{array}$$

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 $$\begin{array}{c}-256x^5-736x^4+31x^3-190x^2+10x+\log (x)\end{array}$$

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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