3.42.83 $\int \frac{-20x+2x^2+(-10x+x^2)\log (2)+(-81+18x)\log (3)}{x^4}dx$

Optimal. Leaf size=30 $$\frac{\frac{(5-x)(2+\log (2))}{x}+\frac{9(3-x)\log (3)}{x^2}}{x}$$

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Rubi [A]  time = 0.02, antiderivative size = 29, normalized size of antiderivative = 0.97, number of steps used = 2, number of rules used = 1, integrand size = 31, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.032, Rules used = {14} $$\begin{array}{c}\frac{27\log (3)}{x^3}+\frac{10-\log \left(\frac{19683}{32}\right)}{x^2}-\frac{2+\log (2)}{x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(-20*x + 2*x^2 + (-10*x + x^2)*Log[2] + (-81 + 18*x)*Log[3])/x^4,x]

[Out]

-((2 + Log[2])/x) + (27*Log[3])/x^3 + (10 - Log[19683/32])/x^2

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (\frac{2+\log (2)}{x^2}-\frac{81\log (3)}{x^4}+\frac{2(-10+\log \left(\frac{19683}{32}\right))}{x^3})dx\\ & =-\frac{2+\log (2)}{x}+\frac{27\log (3)}{x^3}+\frac{10-\log \left(\frac{19683}{32}\right)}{x^2}\end{array}\end{array}$$

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Mathematica [A]  time = 0.02, size = 30, normalized size = 1.00 $$\begin{array}{c}\frac{-2-\log (2)}{x}+\frac{27\log (3)}{x^3}+\frac{10-9\log (3)+\log (32)}{x^2}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-20*x + 2*x^2 + (-10*x + x^2)*Log[2] + (-81 + 18*x)*Log[3])/x^4,x]

[Out]

(-2 - Log[2])/x + (27*Log[3])/x^3 + (10 - 9*Log[3] + Log[32])/x^2

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fricas [A]  time = 0.69, size = 31, normalized size = 1.03 $$\begin{array}{c}-\frac{2x^2+9(x-3)\log (3)+(x^2-5x)\log (2)-10x}{x^3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x-81)*log(3)+(x^2-10*x)*log(2)+2*x^2-20*x)/x^4,x, algorithm="fricas")

[Out]

-(2*x^2 + 9*(x - 3)*log(3) + (x^2 - 5*x)*log(2) - 10*x)/x^3

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giac [A]  time = 0.14, size = 34, normalized size = 1.13 $$\begin{array}{c}-\frac{x^2\log (2)+2x^2+9x\log (3)-5x\log (2)-10x-27\log (3)}{x^3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x-81)*log(3)+(x^2-10*x)*log(2)+2*x^2-20*x)/x^4,x, algorithm="giac")

[Out]

-(x^2*log(2) + 2*x^2 + 9*x*log(3) - 5*x*log(2) - 10*x - 27*log(3))/x^3

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maple [A]  time = 0.04, size = 32, normalized size = 1.07

method	result	size
norman	$\frac{(-2-\ln (2))x^2+(5\ln (2)-9\ln (3)+10)x+27\ln (3)}{x^3}$	$32$
risch	$\frac{(-2-\ln (2))x^2+(5\ln (2)-9\ln (3)+10)x+27\ln (3)}{x^3}$	$32$
default	$\frac{27\ln (3)}{x^3}-\frac{-10\ln (2)+18\ln (3)-20}{2x^2}-\frac{\ln (2)+2}{x}$	$33$
gosper	$-\frac{x^2\ln (2)-5x\ln (2)+9x\ln (3)+2x^2-27\ln (3)-10x}{x^3}$	$35$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((18*x-81)*ln(3)+(x^2-10*x)*ln(2)+2*x^2-20*x)/x^4,x,method=_RETURNVERBOSE)

[Out]

((-2-ln(2))*x^2+(5*ln(2)-9*ln(3)+10)*x+27*ln(3))/x^3

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maxima [A]  time = 0.35, size = 30, normalized size = 1.00 $$\begin{array}{c}-\frac{x^2(\log (2)+2)+x(9\log (3)-5\log (2)-10)-27\log (3)}{x^3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x-81)*log(3)+(x^2-10*x)*log(2)+2*x^2-20*x)/x^4,x, algorithm="maxima")

[Out]

-(x^2*(log(2) + 2) + x*(9*log(3) - 5*log(2) - 10) - 27*log(3))/x^3

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mupad [B]  time = 0.06, size = 24, normalized size = 0.80 $$\begin{array}{c}-\frac{(\ln (2)+2)x^2+(\ln \left(\frac{19683}{32}\right)-10)x-\ln \left(7625597484987\right)}{x^3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(20*x - log(3)*(18*x - 81) + log(2)*(10*x - x^2) - 2*x^2)/x^4,x)

[Out]

-(x^2*(log(2) + 2) - log(7625597484987) + x*(log(19683/32) - 10))/x^3

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sympy [A]  time = 0.49, size = 31, normalized size = 1.03 $$\begin{array}{c}\frac{x^2(-2-\log (2))+x(-9\log (3)+5\log (2)+10)+27\log (3)}{x^3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x-81)*ln(3)+(x**2-10*x)*ln(2)+2*x**2-20*x)/x**4,x)

[Out]

(x**2*(-2 - log(2)) + x*(-9*log(3) + 5*log(2) + 10) + 27*log(3))/x**3

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