\(\int (-1-2 x+5 \log (x)) \, dx\) [8339]

Optimal result

Integrand size = 9, antiderivative size = 15 \[ \int (-1-2 x+5 \log (x)) \, dx=-5+x (-1-x+5 (-1+\log (x))) \]

[Out]

x*(5*ln(x)-6-x)-5

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2332} \[ \int (-1-2 x+5 \log (x)) \, dx=-x^2-6 x+5 x \log (x) \]

[In]

Int[-1 - 2*x + 5*Log[x],x]

[Out]

-6*x - x^2 + 5*x*Log[x]

Rule 2332

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps \begin{align*} \text {integral}& = -x-x^2+5 \int \log (x) \, dx \\ & = -6 x-x^2+5 x \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int (-1-2 x+5 \log (x)) \, dx=-6 x-x^2+5 x \log (x) \]

[In]

Integrate[-1 - 2*x + 5*Log[x],x]

[Out]

-6*x - x^2 + 5*x*Log[x]

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00

method	result	size
default	\(-x^{2}-6 x +5 x \ln \left (x \right )\)	\(15\)
norman	\(-x^{2}-6 x +5 x \ln \left (x \right )\)	\(15\)
risch	\(-x^{2}-6 x +5 x \ln \left (x \right )\)	\(15\)
parallelrisch	\(-x^{2}-6 x +5 x \ln \left (x \right )\)	\(15\)
parts	\(-x^{2}-6 x +5 x \ln \left (x \right )\)	\(15\)

[In]

int(5*ln(x)-2*x-1,x,method=_RETURNVERBOSE)

[Out]

-x^2-6*x+5*x*ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int (-1-2 x+5 \log (x)) \, dx=-x^{2} + 5 \, x \log \left (x\right ) - 6 \, x \]

[In]

integrate(5*log(x)-2*x-1,x, algorithm="fricas")

[Out]

-x^2 + 5*x*log(x) - 6*x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int (-1-2 x+5 \log (x)) \, dx=- x^{2} + 5 x \log {\left (x \right )} - 6 x \]

[In]

integrate(5*ln(x)-2*x-1,x)

[Out]

-x**2 + 5*x*log(x) - 6*x

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int (-1-2 x+5 \log (x)) \, dx=-x^{2} + 5 \, x \log \left (x\right ) - 6 \, x \]

[In]

integrate(5*log(x)-2*x-1,x, algorithm="maxima")

[Out]

-x^2 + 5*x*log(x) - 6*x

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int (-1-2 x+5 \log (x)) \, dx=-x^{2} + 5 \, x \log \left (x\right ) - 6 \, x \]

[In]

integrate(5*log(x)-2*x-1,x, algorithm="giac")

[Out]

-x^2 + 5*x*log(x) - 6*x

Mupad [B] (verification not implemented)

Time = 14.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int (-1-2 x+5 \log (x)) \, dx=-x\,\left (x-5\,\ln \left (x\right )+6\right ) \]

[In]

int(5*log(x) - 2*x - 1,x)

[Out]

-x*(x - 5*log(x) + 6)