3.50.63 \(\int \frac {-24+9 (6-2 x) (6-x)+4 x+(6-x) (i \pi +\log (-2+e^4))}{-6+x} \, dx\)

Optimal. Leaf size=24 \[ x \left (4-i \pi -9 (6-x)-\log \left (-2+e^4\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 2, number of rules used = 1, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {1586} \begin {gather*} 9 x^2-x \left (50+i \pi +\log \left (e^4-2\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-24 + 9*(6 - 2*x)*(6 - x) + 4*x + (6 - x)*(I*Pi + Log[-2 + E^4]))/(-6 + x),x]

[Out]

9*x^2 - x*(50 + I*Pi + Log[-2 + E^4])

Rule 1586

Int[(u_.)*(Px_)^(p_.)*(Qx_)^(q_.), x_Symbol] :> Int[u*PolynomialQuotient[Px, Qx, x]^p*Qx^(p + q), x] /; FreeQ[
q, x] && PolyQ[Px, x] && PolyQ[Qx, x] && EqQ[PolynomialRemainder[Px, Qx, x], 0] && IntegerQ[p] && LtQ[p*q, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-50-i \pi +18 x-\log \left (-2+e^4\right )\right ) \, dx\\ &=9 x^2-x \left (50+i \pi +\log \left (-2+e^4\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 24, normalized size = 1.00 \begin {gather*} -50 x-i \pi x+9 x^2-x \log \left (-2+e^4\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-24 + 9*(6 - 2*x)*(6 - x) + 4*x + (6 - x)*(I*Pi + Log[-2 + E^4]))/(-6 + x),x]

[Out]

-50*x - I*Pi*x + 9*x^2 - x*Log[-2 + E^4]

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fricas [A]  time = 0.89, size = 19, normalized size = 0.79 \begin {gather*} 9 \, x^{2} - x \log \left (-e^{4} + 2\right ) - 50 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6-2*x)*exp(log(-x+6)+2*log(3))+(-x+6)*log(2-exp(4))+4*x-24)/(x-6),x, algorithm="fricas")

[Out]

9*x^2 - x*log(-e^4 + 2) - 50*x

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giac [A]  time = 0.15, size = 19, normalized size = 0.79 \begin {gather*} 9 \, x^{2} - x \log \left (-e^{4} + 2\right ) - 50 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6-2*x)*exp(log(-x+6)+2*log(3))+(-x+6)*log(2-exp(4))+4*x-24)/(x-6),x, algorithm="giac")

[Out]

9*x^2 - x*log(-e^4 + 2) - 50*x

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maple [A]  time = 0.12, size = 20, normalized size = 0.83

method	result	size
default	\(9 x^{2}-50 x -\ln \left (2-{\mathrm e}^{4}\right ) x\)	\(20\)
norman	\(\left (-50-\ln \left (2-{\mathrm e}^{4}\right )\right ) x +9 x^{2}\)	\(20\)
risch	\(9 x^{2}-50 x -\ln \left (2-{\mathrm e}^{4}\right ) x\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((6-2*x)*exp(ln(-x+6)+2*ln(3))+(-x+6)*ln(2-exp(4))+4*x-24)/(x-6),x,method=_RETURNVERBOSE)

[Out]

9*x^2-50*x-ln(2-exp(4))*x

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maxima [A]  time = 0.48, size = 18, normalized size = 0.75 \begin {gather*} 9 \, x^{2} - x {\left (\log \left (-e^{4} + 2\right ) + 50\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6-2*x)*exp(log(-x+6)+2*log(3))+(-x+6)*log(2-exp(4))+4*x-24)/(x-6),x, algorithm="maxima")

[Out]

9*x^2 - x*(log(-e^4 + 2) + 50)

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mupad [B]  time = 0.06, size = 18, normalized size = 0.75 \begin {gather*} 9\,x^2-x\,\left (\ln \left (2-{\mathrm {e}}^4\right )+50\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(2 - exp(4))*(x - 6) - 4*x + exp(2*log(3) + log(6 - x))*(2*x - 6) + 24)/(x - 6),x)

[Out]

9*x^2 - x*(log(2 - exp(4)) + 50)

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sympy [A]  time = 0.09, size = 19, normalized size = 0.79 \begin {gather*} 9 x^{2} + x \left (-50 - \log {\left (-2 + e^{4} \right )} - i \pi \right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6-2*x)*exp(ln(-x+6)+2*ln(3))+(-x+6)*ln(2-exp(4))+4*x-24)/(x-6),x)

[Out]

9*x**2 + x*(-50 - log(-2 + exp(4)) - I*pi)

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