3.69.31 $\int (1-6e^9+9e^{18}-\log (4)+(2-6e^9)\log (x)+{\log }^2(x))dx$

Optimal. Leaf size=22 $$-3+x-x\log (4)+x{(3e^9-\log (x))}^2$$

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Rubi [B]  time = 0.02, antiderivative size = 55, normalized size of antiderivative = 2.50, number of steps used = 4, number of rules used = 2, integrand size = 30, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.067, Rules used = {2295, 2296} $$\begin{array}{c}-2(1-3e^9)x+2x+x{\log }^2(x)+2(1-3e^9)x\log (x)-2x\log (x)+x(1-6e^9+9e^{18}-\log (4))\end{array}$$

Antiderivative was successfully verified.

[In]

Int[1 - 6*E^9 + 9*E^18 - Log[4] + (2 - 6*E^9)*Log[x] + Log[x]^2,x]

[Out]

2*x - 2*(1 - 3*E^9)*x + x*(1 - 6*E^9 + 9*E^18 - Log[4]) - 2*x*Log[x] + 2*(1 - 3*E^9)*x*Log[x] + x*Log[x]^2

Rule 2295

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

Rule 2296

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =x(1-6e^9+9e^{18}-\log (4))+\left(2(1-3e^9)\right)\int \log (x)dx+\int {\log }^2(x)dx\\ & =-2(1-3e^9)x+x(1-6e^9+9e^{18}-\log (4))+2(1-3e^9)x\log (x)+x{\log }^2(x)-2\int \log (x)dx\\ & =2x-2(1-3e^9)x+x(1-6e^9+9e^{18}-\log (4))-2x\log (x)+2(1-3e^9)x\log (x)+x{\log }^2(x)\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 27, normalized size = 1.23 $$\begin{array}{c}x+9e^{18}x-x\log (4)-6e^{9}x\log (x)+x{\log }^2(x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[1 - 6*E^9 + 9*E^18 - Log[4] + (2 - 6*E^9)*Log[x] + Log[x]^2,x]

[Out]

x + 9*E^18*x - x*Log[4] - 6*E^9*x*Log[x] + x*Log[x]^2

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fricas [A]  time = 1.03, size = 25, normalized size = 1.14 $$\begin{array}{c}-6x{e}^9\log (x)+x\log (x{)}^2+9x{e}^{18}-2x\log (2)+x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)^2+(-6*exp(9)+2)*log(x)-2*log(2)+9*exp(9)^2-6*exp(9)+1,x, algorithm="fricas")

[Out]

-6*x*e^9*log(x) + x*log(x)^2 + 9*x*e^18 - 2*x*log(2) + x

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giac [B]  time = 0.12, size = 46, normalized size = 2.09 $$\begin{array}{c}x\log (x{)}^2-2(x\log (x)-x)(3e^9-1)+9x{e}^{18}-6x{e}^9-2x\log (2)-2x\log (x)+3x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)^2+(-6*exp(9)+2)*log(x)-2*log(2)+9*exp(9)^2-6*exp(9)+1,x, algorithm="giac")

[Out]

x*log(x)^2 - 2*(x*log(x) - x)*(3*e^9 - 1) + 9*x*e^18 - 6*x*e^9 - 2*x*log(2) - 2*x*log(x) + 3*x

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maple [A]  time = 0.02, size = 26, normalized size = 1.18

method	result	size
risch	$x+x\ln (x{)}^2-6x{\mathrm{e}}^9\ln (x)+9{\mathrm{e}}^{18}x-2x\ln (2)$	$26$
default	$x+x\ln (x{)}^2-6x{\mathrm{e}}^9\ln (x)+9{\mathrm{e}}^{18}x-2x\ln (2)$	$28$
norman	$x\ln (x{)}^2+(1+9{\mathrm{e}}^{18}-2\ln (2))x-6x{\mathrm{e}}^9\ln (x)$	$29$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(x)^2+(-6*exp(9)+2)*ln(x)-2*ln(2)+9*exp(9)^2-6*exp(9)+1,x,method=_RETURNVERBOSE)

[Out]

x+x*ln(x)^2-6*x*exp(9)*ln(x)+9*exp(18)*x-2*x*ln(2)

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maxima [B]  time = 0.37, size = 45, normalized size = 2.05 $$\begin{array}{c}(\log (x{)}^2-2\log (x)+2)x-2(x\log (x)-x)(3e^9-1)+9x{e}^{18}-6x{e}^9-2x\log (2)+x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)^2+(-6*exp(9)+2)*log(x)-2*log(2)+9*exp(9)^2-6*exp(9)+1,x, algorithm="maxima")

[Out]

(log(x)^2 - 2*log(x) + 2)*x - 2*(x*log(x) - x)*(3*e^9 - 1) + 9*x*e^18 - 6*x*e^9 - 2*x*log(2) + x

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mupad [B]  time = 4.14, size = 22, normalized size = 1.00 $$\begin{array}{c}x({\ln (x)}^2-6{\mathrm{e}}^9\ln (x)+9{\mathrm{e}}^{18}-\ln (4)+1)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(9*exp(18) - 6*exp(9) - 2*log(2) + log(x)^2 - log(x)*(6*exp(9) - 2) + 1,x)

[Out]

x*(9*exp(18) - log(4) + log(x)^2 - 6*exp(9)*log(x) + 1)

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sympy [A]  time = 0.15, size = 29, normalized size = 1.32 $$\begin{array}{c}x\log {(x)}^2-6x{e}^9\log (x)+x(-2\log (2)+1+9e^{18})\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(x)**2+(-6*exp(9)+2)*ln(x)-2*ln(2)+9*exp(9)**2-6*exp(9)+1,x)

[Out]

x*log(x)**2 - 6*x*exp(9)*log(x) + x*(-2*log(2) + 1 + 9*exp(18))

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