\(\int (20 e^x-20 \log (x)) \, dx\) [8524]

Optimal result

Integrand size = 10, antiderivative size = 16 \[ \int \left (20 e^x-20 \log (x)\right ) \, dx=20 x \left (1+\frac {e^x}{x}-\log (x)\right ) \]

[Out]

20*(1+exp(x)/x-ln(x))*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2225, 2332} \[ \int \left (20 e^x-20 \log (x)\right ) \, dx=20 x+20 e^x-20 x \log (x) \]

[In]

Int[20*E^x - 20*Log[x],x]

[Out]

20*E^x + 20*x - 20*x*Log[x]

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, 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}& = 20 \int e^x \, dx-20 \int \log (x) \, dx \\ & = 20 e^x+20 x-20 x \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (20 e^x-20 \log (x)\right ) \, dx=20 \left (e^x+x-x \log (x)\right ) \]

[In]

Integrate[20*E^x - 20*Log[x],x]

[Out]

20*(E^x + x - x*Log[x])

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88

method	result	size
default	\(20 x -20 x \ln \left (x \right )+20 \,{\mathrm e}^{x}\)	\(14\)
norman	\(20 x -20 x \ln \left (x \right )+20 \,{\mathrm e}^{x}\)	\(14\)
risch	\(20 x -20 x \ln \left (x \right )+20 \,{\mathrm e}^{x}\)	\(14\)
parallelrisch	\(20 x -20 x \ln \left (x \right )+20 \,{\mathrm e}^{x}\)	\(14\)
parts	\(20 x -20 x \ln \left (x \right )+20 \,{\mathrm e}^{x}\)	\(14\)

[In]

int(-20*ln(x)+20*exp(x),x,method=_RETURNVERBOSE)

[Out]

20*x-20*x*ln(x)+20*exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \left (20 e^x-20 \log (x)\right ) \, dx=-20 \, x \log \left (x\right ) + 20 \, x + 20 \, e^{x} \]

[In]

integrate(-20*log(x)+20*exp(x),x, algorithm="fricas")

[Out]

-20*x*log(x) + 20*x + 20*e^x

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \left (20 e^x-20 \log (x)\right ) \, dx=- 20 x \log {\left (x \right )} + 20 x + 20 e^{x} \]

[In]

integrate(-20*ln(x)+20*exp(x),x)

[Out]

-20*x*log(x) + 20*x + 20*exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \left (20 e^x-20 \log (x)\right ) \, dx=-20 \, x \log \left (x\right ) + 20 \, x + 20 \, e^{x} \]

[In]

integrate(-20*log(x)+20*exp(x),x, algorithm="maxima")

[Out]

-20*x*log(x) + 20*x + 20*e^x

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \left (20 e^x-20 \log (x)\right ) \, dx=-20 \, x \log \left (x\right ) + 20 \, x + 20 \, e^{x} \]

[In]

integrate(-20*log(x)+20*exp(x),x, algorithm="giac")

[Out]

-20*x*log(x) + 20*x + 20*e^x

Mupad [B] (verification not implemented)

Time = 12.92 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \left (20 e^x-20 \log (x)\right ) \, dx=20\,x+20\,{\mathrm {e}}^x-20\,x\,\ln \left (x\right ) \]

[In]

int(20*exp(x) - 20*log(x),x)

[Out]

20*x + 20*exp(x) - 20*x*log(x)