\(\int \frac {1+x}{x} \, dx\) [9073]

Optimal result

Integrand size = 7, antiderivative size = 10 \[ \int \frac {1+x}{x} \, dx=-\frac {28}{3}+\frac {1}{e^3}+x+\log (x) \]

[Out]

1/exp(3)-28/3+ln(x)+x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.40, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {45} \[ \int \frac {1+x}{x} \, dx=x+\log (x) \]

[In]

Int[(1 + x)/x,x]

[Out]

x + Log[x]

Rule 45

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{align*} \text {integral}& = \int \left (1+\frac {1}{x}\right ) \, dx \\ & = x+\log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.40 \[ \int \frac {1+x}{x} \, dx=x+\log (x) \]

[In]

Integrate[(1 + x)/x,x]

[Out]

x + Log[x]

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50

method	result	size
default	\(x +\ln \left (x \right )\)	\(5\)
norman	\(x +\ln \left (x \right )\)	\(5\)
risch	\(x +\ln \left (x \right )\)	\(5\)
parallelrisch	\(x +\ln \left (x \right )\)	\(5\)

[In]

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

[Out]

x+ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.40 \[ \int \frac {1+x}{x} \, dx=x + \log \left (x\right ) \]

[In]

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

[Out]

x + log(x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.30 \[ \int \frac {1+x}{x} \, dx=x + \log {\left (x \right )} \]

[In]

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

[Out]

x + log(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.40 \[ \int \frac {1+x}{x} \, dx=x + \log \left (x\right ) \]

[In]

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

[Out]

x + log(x)

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1+x}{x} \, dx=x + \log \left ({\left | x \right |}\right ) \]

[In]

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

[Out]

x + log(abs(x))

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.40 \[ \int \frac {1+x}{x} \, dx=x+\ln \left (x\right ) \]

[In]

int((x + 1)/x,x)

[Out]

x + log(x)