3.46.35 \(\int \frac {2+40 x^3-40 x^4+(-30 x^2+30 x^3) \log (4)}{-1+x} \, dx\)

Optimal. Leaf size=19 \[ 2 \left (-1+5 x^3 (-x+\log (4))+\log (-1+x)\right ) \]

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Rubi [A]  time = 0.04, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 2, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {1850} \begin {gather*} -10 x^4+10 x^3 \log (4)+2 \log (1-x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2 + 40*x^3 - 40*x^4 + (-30*x^2 + 30*x^3)*Log[4])/(-1 + x),x]

[Out]

-10*x^4 + 10*x^3*Log[4] + 2*Log[1 - x]

Rule 1850

Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x^n)^p, x], x] /; FreeQ[
{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p, 0] || EqQ[n, 1])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2}{-1+x}-40 x^3+30 x^2 \log (4)\right ) \, dx\\ &=-10 x^4+10 x^3 \log (4)+2 \log (1-x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 23, normalized size = 1.21 \begin {gather*} 10-10 x^4-\log (1048576)+x^3 \log (1048576)+2 \log (-1+x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2 + 40*x^3 - 40*x^4 + (-30*x^2 + 30*x^3)*Log[4])/(-1 + x),x]

[Out]

10 - 10*x^4 - Log[1048576] + x^3*Log[1048576] + 2*Log[-1 + x]

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fricas [A]  time = 0.73, size = 19, normalized size = 1.00 \begin {gather*} -10 \, x^{4} + 20 \, x^{3} \log \relax (2) + 2 \, \log \left (x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(30*x^3-30*x^2)*log(2)-40*x^4+40*x^3+2)/(x-1),x, algorithm="fricas")

[Out]

-10*x^4 + 20*x^3*log(2) + 2*log(x - 1)

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giac [A]  time = 0.13, size = 20, normalized size = 1.05 \begin {gather*} -10 \, x^{4} + 20 \, x^{3} \log \relax (2) + 2 \, \log \left ({\left | x - 1 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(30*x^3-30*x^2)*log(2)-40*x^4+40*x^3+2)/(x-1),x, algorithm="giac")

[Out]

-10*x^4 + 20*x^3*log(2) + 2*log(abs(x - 1))

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maple [A]  time = 0.17, size = 20, normalized size = 1.05

method	result	size
default	\(-10 x^{4}+20 x^{3} \ln \relax (2)+2 \ln \left (x -1\right )\)	\(20\)
norman	\(-10 x^{4}+20 x^{3} \ln \relax (2)+2 \ln \left (x -1\right )\)	\(20\)
risch	\(-10 x^{4}+20 x^{3} \ln \relax (2)+2 \ln \left (x -1\right )\)	\(20\)
meijerg	\(-38 \ln \left (1-x \right )-\frac {2 x \left (15 x^{3}+20 x^{2}+30 x +60\right )}{3}-\left (60 \ln \relax (2)+40\right ) \left (-\frac {x \left (4 x^{2}+6 x +12\right )}{12}-\ln \left (1-x \right )\right )-60 \ln \relax (2) \left (\frac {x \left (6+3 x \right )}{6}+\ln \left (1-x \right )\right )\)	\(77\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*(30*x^3-30*x^2)*ln(2)-40*x^4+40*x^3+2)/(x-1),x,method=_RETURNVERBOSE)

[Out]

-10*x^4+20*x^3*ln(2)+2*ln(x-1)

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maxima [A]  time = 0.39, size = 19, normalized size = 1.00 \begin {gather*} -10 \, x^{4} + 20 \, x^{3} \log \relax (2) + 2 \, \log \left (x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(30*x^3-30*x^2)*log(2)-40*x^4+40*x^3+2)/(x-1),x, algorithm="maxima")

[Out]

-10*x^4 + 20*x^3*log(2) + 2*log(x - 1)

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mupad [B]  time = 0.05, size = 19, normalized size = 1.00 \begin {gather*} 2\,\ln \left (x-1\right )+20\,x^3\,\ln \relax (2)-10\,x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*log(2)*(30*x^2 - 30*x^3) - 40*x^3 + 40*x^4 - 2)/(x - 1),x)

[Out]

2*log(x - 1) + 20*x^3*log(2) - 10*x^4

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sympy [A]  time = 0.09, size = 19, normalized size = 1.00 \begin {gather*} - 10 x^{4} + 20 x^{3} \log {\relax (2 )} + 2 \log {\left (x - 1 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(30*x**3-30*x**2)*ln(2)-40*x**4+40*x**3+2)/(x-1),x)

[Out]

-10*x**4 + 20*x**3*log(2) + 2*log(x - 1)

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