3.25.15 \(\int (28+18 x+4 \log (x)) \, dx\)

Optimal. Leaf size=18 \[ 4+e^e+5 x^2+4 x (6+x+\log (x)) \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2295} \begin {gather*} 9 x^2+24 x+4 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[28 + 18*x + 4*Log[x],x]

[Out]

24*x + 9*x^2 + 4*x*Log[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} &=28 x+9 x^2+4 \int \log (x) \, dx\\ &=24 x+9 x^2+4 x \log (x)\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 14, normalized size = 0.78 \begin {gather*} 24 x+9 x^2+4 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[28 + 18*x + 4*Log[x],x]

[Out]

24*x + 9*x^2 + 4*x*Log[x]

________________________________________________________________________________________

fricas [A]  time = 0.57, size = 14, normalized size = 0.78 \begin {gather*} 9 \, x^{2} + 4 \, x \log \relax (x) + 24 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(x)+18*x+28,x, algorithm="fricas")

[Out]

9*x^2 + 4*x*log(x) + 24*x

________________________________________________________________________________________

giac [A]  time = 0.20, size = 14, normalized size = 0.78 \begin {gather*} 9 \, x^{2} + 4 \, x \log \relax (x) + 24 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(x)+18*x+28,x, algorithm="giac")

[Out]

9*x^2 + 4*x*log(x) + 24*x

________________________________________________________________________________________

maple [A]  time = 0.04, size = 15, normalized size = 0.83

method	result	size
default	\(9 x^{2}+24 x +4 x \ln \relax (x )\)	\(15\)
norman	\(9 x^{2}+24 x +4 x \ln \relax (x )\)	\(15\)
risch	\(9 x^{2}+24 x +4 x \ln \relax (x )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*ln(x)+18*x+28,x,method=_RETURNVERBOSE)

[Out]

9*x^2+24*x+4*x*ln(x)

________________________________________________________________________________________

maxima [A]  time = 0.51, size = 14, normalized size = 0.78 \begin {gather*} 9 \, x^{2} + 4 \, x \log \relax (x) + 24 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(x)+18*x+28,x, algorithm="maxima")

[Out]

9*x^2 + 4*x*log(x) + 24*x

________________________________________________________________________________________

mupad [B]  time = 1.36, size = 11, normalized size = 0.61 \begin {gather*} x\,\left (9\,x+4\,\ln \relax (x)+24\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(18*x + 4*log(x) + 28,x)

[Out]

x*(9*x + 4*log(x) + 24)

________________________________________________________________________________________

sympy [A]  time = 0.08, size = 14, normalized size = 0.78 \begin {gather*} 9 x^{2} + 4 x \log {\relax (x )} + 24 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*ln(x)+18*x+28,x)

[Out]

9*x**2 + 4*x*log(x) + 24*x

________________________________________________________________________________________