3.86.24 \(\int (20 e^x-20 \log (x)) \, dx\)

Optimal. Leaf size=16 \[ 20 x \left (1+\frac {e^x}{x}-\log (x)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2194, 2295} \begin {gather*} 20 x+20 e^x-20 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[20*E^x - 20*Log[x],x]

[Out]

20*E^x + 20*x - 20*x*Log[x]

Rule 2194

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 2295

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 {gather*} \begin {aligned} \text {integral} &=20 \int e^x \, dx-20 \int \log (x) \, dx\\ &=20 e^x+20 x-20 x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.75 \begin {gather*} 20 \left (e^x+x-x \log (x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[20*E^x - 20*Log[x],x]

[Out]

20*(E^x + x - x*Log[x])

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fricas [A]  time = 0.66, size = 13, normalized size = 0.81 \begin {gather*} -20 \, x \log \relax (x) + 20 \, x + 20 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x*log(x) + 20*x + 20*e^x

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giac [A]  time = 0.14, size = 13, normalized size = 0.81 \begin {gather*} -20 \, x \log \relax (x) + 20 \, x + 20 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x*log(x) + 20*x + 20*e^x

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maple [A]  time = 0.02, size = 14, normalized size = 0.88

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.36, size = 13, normalized size = 0.81 \begin {gather*} -20 \, x \log \relax (x) + 20 \, x + 20 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x*log(x) + 20*x + 20*e^x

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mupad [B]  time = 5.29, size = 13, normalized size = 0.81 \begin {gather*} 20\,x+20\,{\mathrm {e}}^x-20\,x\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(20*exp(x) - 20*log(x),x)

[Out]

20*x + 20*exp(x) - 20*x*log(x)

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sympy [A]  time = 0.24, size = 14, normalized size = 0.88 \begin {gather*} - 20 x \log {\relax (x )} + 20 x + 20 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-20*x*log(x) + 20*x + 20*exp(x)

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