3.41.86 $\int \frac{2-3x}{x}dx$

Optimal. Leaf size=18 $$-3x+\log \left(\frac{2e^8{x}^2}{-1+e}\right)$$

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.44, number of steps used = 2, number of rules used = 1, integrand size = 9, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.111, Rules used = {43} $$\begin{array}{c}2\log (x)-3x\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(2 - 3*x)/x,x]

[Out]

-3*x + 2*Log[x]

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.44 $$\begin{array}{c}-3x+2\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(2 - 3*x)/x,x]

[Out]

-3*x + 2*Log[x]

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fricas [A]  time = 0.96, size = 8, normalized size = 0.44 $$\begin{array}{c}-3x+2\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + 2*log(x)

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giac [A]  time = 0.14, size = 9, normalized size = 0.50 $$\begin{array}{c}-3x+2\log \left(\left|x\right|\right)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + 2*log(abs(x))

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maple [A]  time = 0.01, size = 9, normalized size = 0.50

method	result	size
default	$-3x+2\ln (x)$	$9$
norman	$-3x+2\ln (x)$	$9$
risch	$-3x+2\ln (x)$	$9$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x+2*ln(x)

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maxima [A]  time = 0.37, size = 8, normalized size = 0.44 $$\begin{array}{c}-3x+2\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + 2*log(x)

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mupad [B]  time = 0.02, size = 8, normalized size = 0.44 $$\begin{array}{c}2\ln (x)-3x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*x - 2)/x,x)

[Out]

2*log(x) - 3*x

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sympy [A]  time = 0.06, size = 7, normalized size = 0.39 $$\begin{array}{c}-3x+2\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x + 2*log(x)

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