3.14.3 $\int \frac{1+x}{x}dx$

Optimal. Leaf size=10 $$6+e^{15}+x+\log (2x)$$

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Rubi [A]  time = 0.00, antiderivative size = 4, normalized size of antiderivative = 0.40, number of steps used = 2, number of rules used = 1, integrand size = 7, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.143, Rules used = {43} $$\begin{array}{c}x+\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(1 + x)/x,x]

[Out]

x + 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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (1+\frac{1}{x})dx\\ & =x+\log (x)\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 4, normalized size = 0.40 $$\begin{array}{c}x+\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(1 + x)/x,x]

[Out]

x + Log[x]

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fricas [A]  time = 0.74, size = 4, normalized size = 0.40 $$\begin{array}{c}x+\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x+1)/x,x, algorithm="fricas")

[Out]

x + log(x)

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giac [A]  time = 0.37, size = 5, normalized size = 0.50 $$\begin{array}{c}x+\log \left(\left|x\right|\right)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x+1)/x,x, algorithm="giac")

[Out]

x + log(abs(x))

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maple [A]  time = 0.01, size = 5, normalized size = 0.50

method	result	size
default	$x+\ln (x)$	$5$
norman	$x+\ln (x)$	$5$
risch	$x+\ln (x)$	$5$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x+1)/x,x,method=_RETURNVERBOSE)

[Out]

x+ln(x)

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maxima [A]  time = 0.39, size = 4, normalized size = 0.40 $$\begin{array}{c}x+\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x+1)/x,x, algorithm="maxima")

[Out]

x + log(x)

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mupad [B]  time = 0.01, size = 4, normalized size = 0.40 $$\begin{array}{c}x+\ln (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + 1)/x,x)

[Out]

x + log(x)

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sympy [A]  time = 0.06, size = 3, normalized size = 0.30 $$\begin{array}{c}x+\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x+1)/x,x)

[Out]

x + log(x)

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