3.67.9 $\int \frac{2x^3-2\log (3)}{x^3}dx$

Optimal. Leaf size=16 $$-1-e^2+2x+\frac{\log (3)}{x^2}$$

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.81, number of steps used = 2, number of rules used = 1, integrand size = 14, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.071, Rules used = {14} $$\begin{array}{c}\frac{\log (9)}{2x^2}+2x\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(2*x^3 - 2*Log[3])/x^3,x]

[Out]

2*x + Log[9]/(2*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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (2-\frac{\log (9)}{x^3})dx\\ & =2x+\frac{\log (9)}{2x^2}\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.81 $$\begin{array}{c}2x+\frac{\log (9)}{2x^2}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(2*x^3 - 2*Log[3])/x^3,x]

[Out]

2*x + Log[9]/(2*x^2)

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fricas [A]  time = 0.58, size = 12, normalized size = 0.75 $$\begin{array}{c}\frac{2x^3+\log (3)}{x^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(2*x^3 + log(3))/x^2

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giac [A]  time = 0.14, size = 10, normalized size = 0.62 $$\begin{array}{c}2x+\frac{\log (3)}{x^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x + log(3)/x^2

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maple [A]  time = 0.06, size = 11, normalized size = 0.69

method	result	size
default	$2x+\frac{\ln (3)}{x^2}$	$11$
risch	$2x+\frac{\ln (3)}{x^2}$	$11$
gosper	$\frac{2x^3+\ln (3)}{x^2}$	$13$
norman	$\frac{2x^3+\ln (3)}{x^2}$	$13$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2*ln(3)+2*x^3)/x^3,x,method=_RETURNVERBOSE)

[Out]

2*x+1/x^2*ln(3)

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maxima [A]  time = 0.37, size = 10, normalized size = 0.62 $$\begin{array}{c}2x+\frac{\log (3)}{x^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*x + log(3)/x^2

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mupad [B]  time = 4.26, size = 10, normalized size = 0.62 $$\begin{array}{c}2x+\frac{\ln (3)}{x^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*log(3) - 2*x^3)/x^3,x)

[Out]

2*x + log(3)/x^2

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sympy [A]  time = 0.08, size = 8, normalized size = 0.50 $$\begin{array}{c}2x+\frac{\log (3)}{x^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*ln(3)+2*x**3)/x**3,x)

[Out]

2*x + log(3)/x**2

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