3.47.53 \(\int (17640-4410 x+2 x \log (3)) \, dx\)

Optimal. Leaf size=15 \[ x^2 \left (-\frac {2205 (-8+x)}{x}+\log (3)\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {6} \begin {gather*} 17640 x-x^2 (2205-\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[17640 - 4410*x + 2*x*Log[3],x]

[Out]

17640*x - x^2*(2205 - Log[3])

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int (17640+x (-4410+2 \log (3))) \, dx\\ &=17640 x-x^2 (2205-\log (3))\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} 17640 x-2205 x^2+x^2 \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[17640 - 4410*x + 2*x*Log[3],x]

[Out]

17640*x - 2205*x^2 + x^2*Log[3]

________________________________________________________________________________________

fricas [A]  time = 0.60, size = 15, normalized size = 1.00 \begin {gather*} x^{2} \log \relax (3) - 2205 \, x^{2} + 17640 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x*log(3)-4410*x+17640,x, algorithm="fricas")

[Out]

x^2*log(3) - 2205*x^2 + 17640*x

________________________________________________________________________________________

giac [A]  time = 0.13, size = 15, normalized size = 1.00 \begin {gather*} x^{2} \log \relax (3) - 2205 \, x^{2} + 17640 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x*log(3)-4410*x+17640,x, algorithm="giac")

[Out]

x^2*log(3) - 2205*x^2 + 17640*x

________________________________________________________________________________________

maple [A]  time = 0.02, size = 12, normalized size = 0.80

method	result	size
gosper	\(x \left (x \ln \relax (3)-2205 x +17640\right )\)	\(12\)
norman	\(\left (\ln \relax (3)-2205\right ) x^{2}+17640 x\)	\(13\)
default	\(x^{2} \ln \relax (3)-2205 x^{2}+17640 x\)	\(16\)
risch	\(x^{2} \ln \relax (3)-2205 x^{2}+17640 x\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x*ln(3)-4410*x+17640,x,method=_RETURNVERBOSE)

[Out]

x*(x*ln(3)-2205*x+17640)

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 15, normalized size = 1.00 \begin {gather*} x^{2} \log \relax (3) - 2205 \, x^{2} + 17640 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x*log(3)-4410*x+17640,x, algorithm="maxima")

[Out]

x^2*log(3) - 2205*x^2 + 17640*x

________________________________________________________________________________________

mupad [B]  time = 0.02, size = 12, normalized size = 0.80 \begin {gather*} \left (\ln \relax (3)-2205\right )\,x^2+17640\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x*log(3) - 4410*x + 17640,x)

[Out]

17640*x + x^2*(log(3) - 2205)

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 10, normalized size = 0.67 \begin {gather*} x^{2} \left (-2205 + \log {\relax (3 )}\right ) + 17640 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x*ln(3)-4410*x+17640,x)

[Out]

x**2*(-2205 + log(3)) + 17640*x

________________________________________________________________________________________