3.24.57 \(\int \frac {1}{\sqrt [4]{-1+3 x-3 x^2+x^3} (-1-2 x+x^2+3 x^3)^4} \, dx\)

Optimal. Leaf size=187 \[ \frac {\left ((x-1)^3\right )^{3/4} \left (\frac {\sqrt [4]{x-1} \left (-5094769914 x^8-2006712954 x^7+9762576651 x^6+5802065412 x^5-5857310139 x^4-4979849490 x^3+596630756 x^2+1357068302 x+307788101\right )}{2859936 \left (3 x^3+x^2-2 x-1\right )^3}-\frac {\text {RootSum}\left [3 \text {$\#$1}^{12}+10 \text {$\#$1}^8+9 \text {$\#$1}^4+1\& ,\frac {566085546 \text {$\#$1}^8 \log \left (\sqrt [4]{x-1}-\text {$\#$1}\right )-234521814 \text {$\#$1}^4 \log \left (\sqrt [4]{x-1}-\text {$\#$1}\right )-41317673 \log \left (\sqrt [4]{x-1}-\text {$\#$1}\right )}{9 \text {$\#$1}^{11}+20 \text {$\#$1}^7+9 \text {$\#$1}^3}\& \right ]}{3813248}\right )}{(x-1)^{9/4}} \]

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Rubi [F]  time = 0.10, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{\sqrt [4]{-1+3 x-3 x^2+x^3} \left (-1-2 x+x^2+3 x^3\right )^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

\begin {align*} \int \frac {1}{\sqrt [4]{-1+3 x-3 x^2+x^3} \left (-1-2 x+x^2+3 x^3\right )^4} \, dx &=\int \frac {1}{\sqrt [4]{-1+3 x-3 x^2+x^3} \left (-1-2 x+x^2+3 x^3\right )^4} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.16, size = 186, normalized size = 0.99 \begin {gather*} \frac {(x-1)^{3/4} \left (-3 \text {RootSum}\left [3 \text {$\#$1}^{12}+10 \text {$\#$1}^8+9 \text {$\#$1}^4+1\&,\frac {566085546 \text {$\#$1}^8 \log \left (\sqrt [4]{x-1}-\text {$\#$1}\right )-234521814 \text {$\#$1}^4 \log \left (\sqrt [4]{x-1}-\text {$\#$1}\right )-41317673 \log \left (\sqrt [4]{x-1}-\text {$\#$1}\right )}{9 \text {$\#$1}^{11}+20 \text {$\#$1}^7+9 \text {$\#$1}^3}\&\right ]-\frac {4 \sqrt [4]{x-1} \left (5094769914 x^8+2006712954 x^7-9762576651 x^6-5802065412 x^5+5857310139 x^4+4979849490 x^3-596630756 x^2-1357068302 x-307788101\right )}{\left (3 x^3+x^2-2 x-1\right )^3}\right )}{11439744 \sqrt [4]{(x-1)^3}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((-1 + x)^(3/4)*((-4*(-1 + x)^(1/4)*(-307788101 - 1357068302*x - 596630756*x^2 + 4979849490*x^3 + 5857310139*x
^4 - 5802065412*x^5 - 9762576651*x^6 + 2006712954*x^7 + 5094769914*x^8))/(-1 - 2*x + x^2 + 3*x^3)^3 - 3*RootSu
m[1 + 9*#1^4 + 10*#1^8 + 3*#1^12 & , (-41317673*Log[(-1 + x)^(1/4) - #1] - 234521814*Log[(-1 + x)^(1/4) - #1]*
#1^4 + 566085546*Log[(-1 + x)^(1/4) - #1]*#1^8)/(9*#1^3 + 20*#1^7 + 9*#1^11) & ]))/(11439744*((-1 + x)^3)^(1/4
))

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IntegrateAlgebraic [A]  time = 18.80, size = 211, normalized size = 1.13 \begin {gather*} \frac {\left ((-1+x)^3\right )^{3/4} \left (-\frac {\left (112513275+3037822236 (-1+x)[phone] (-1+x)^2+130678971480 (-1+x)^3+257277180684 (-1+x)^4+263070561900 (-1+x)^5+146937971619 (-1+x)^6+42764872266 (-1+x)^7+5094769914 (-1+x)^8\right ) \sqrt [4]{-1+x}}{2859936 \left (1+9 (-1+x)+10 (-1+x)^2+3 (-1+x)^3\right )^3}-\frac {\text {RootSum}\left [1+9 \text {$\#$1}^4+10 \text {$\#$1}^8+3 \text {$\#$1}^{12}\&,\frac {-41317673 \log \left (\sqrt [4]{-1+x}-\text {$\#$1}\right )-234521814 \log \left (\sqrt [4]{-1+x}-\text {$\#$1}\right ) \text {$\#$1}^4+566085546 \log \left (\sqrt [4]{-1+x}-\text {$\#$1}\right ) \text {$\#$1}^8}{9 \text {$\#$1}^3+20 \text {$\#$1}^7+9 \text {$\#$1}^{11}}\&\right ]}{3813248}\right )}{(-1+x)^{9/4}} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[1/((-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3)^4),x]

[Out]

(((-1 + x)^3)^(3/4)*(-1/2859936*((112513275 + 3037822236*(-1 + x) + 29822004289*(-1 + x)^2 + 130678971480*(-1
+ x)^3 + 257277180684*(-1 + x)^4 + 263070561900*(-1 + x)^5 + 146937971619*(-1 + x)^6 + 42764872266*(-1 + x)^7
+ 5094769914*(-1 + x)^8)*(-1 + x)^(1/4))/(1 + 9*(-1 + x) + 10*(-1 + x)^2 + 3*(-1 + x)^3)^3 - RootSum[1 + 9*#1^
4 + 10*#1^8 + 3*#1^12 & , (-41317673*Log[(-1 + x)^(1/4) - #1] - 234521814*Log[(-1 + x)^(1/4) - #1]*#1^4 + 5660
85546*Log[(-1 + x)^(1/4) - #1]*#1^8)/(9*#1^3 + 20*#1^7 + 9*#1^11) & ]/3813248))/(-1 + x)^(9/4)

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fricas [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{{\left (3 \, x^{3} + x^{2} - 2 \, x - 1\right )}^{4} {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}^{\frac {1}{4}}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(1/((3*x^3 + x^2 - 2*x - 1)^4*(x^3 - 3*x^2 + 3*x - 1)^(1/4)), x)

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maple [F]  time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (x^{3}-3 x^{2}+3 x -1\right )^{\frac {1}{4}} \left (3 x^{3}+x^{2}-2 x -1\right )^{4}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{{\left (3 \, x^{3} + x^{2} - 2 \, x - 1\right )}^{4} {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}^{\frac {1}{4}}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(1/((3*x^3 + x^2 - 2*x - 1)^4*(x^3 - 3*x^2 + 3*x - 1)^(1/4)), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {1}{{\left (x^3-3\,x^2+3\,x-1\right )}^{1/4}\,{\left (-3\,x^3-x^2+2\,x+1\right )}^4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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