3.10.72 \(\int \frac {\sqrt [4]{-1+3 x-3 x^2+x^3}}{-1-2 x+x^2+3 x^3} \, dx\)
Optimal. Leaf size=74 \[ \frac {\sqrt [4]{(x-1)^3} \text {RootSum}\left [3 \text {$\#$1}^{12}+10 \text {$\#$1}^8+9 \text {$\#$1}^4+1\& ,\frac {\text {$\#$1}^3 \log \left (\sqrt [4]{x-1}-\text {$\#$1}\right )}{9 \text {$\#$1}^8+20 \text {$\#$1}^4+9}\& \right ]}{(x-1)^{3/4}} \]
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Rubi [F] time = 0.11, 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 {\sqrt [4]{-1+3 x-3 x^2+x^3}}{-1-2 x+x^2+3 x^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-1 + 3*x - 3*x^2 + x^3)^(1/4)/(-1 - 2*x + x^2 + 3*x^3),x]
[Out]
Defer[Int][(-1 + 3*x - 3*x^2 + x^3)^(1/4)/(-1 - 2*x + x^2 + 3*x^3), x]
Rubi steps
\begin {align*} \int \frac {\sqrt [4]{-1+3 x-3 x^2+x^3}}{-1-2 x+x^2+3 x^3} \, dx &=\int \frac {\sqrt [4]{-1+3 x-3 x^2+x^3}}{-1-2 x+x^2+3 x^3} \, dx\\ \end {align*}
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Mathematica [A] time = 0.09, size = 74, normalized size = 1.00 \begin {gather*} \frac {\sqrt [4]{(x-1)^3} \text {RootSum}\left [3 \text {$\#$1}^{12}+10 \text {$\#$1}^8+9 \text {$\#$1}^4+1\&,\frac {\text {$\#$1}^3 \log \left (\sqrt [4]{x-1}-\text {$\#$1}\right )}{9 \text {$\#$1}^8+20 \text {$\#$1}^4+9}\&\right ]}{(x-1)^{3/4}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-1 + 3*x - 3*x^2 + x^3)^(1/4)/(-1 - 2*x + x^2 + 3*x^3),x]
[Out]
(((-1 + x)^3)^(1/4)*RootSum[1 + 9*#1^4 + 10*#1^8 + 3*#1^12 & , (Log[(-1 + x)^(1/4) - #1]*#1^3)/(9 + 20*#1^4 +
9*#1^8) & ])/(-1 + x)^(3/4)
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IntegrateAlgebraic [A] time = 10.64, size = 74, normalized size = 1.00 \begin {gather*} \frac {\sqrt [4]{(-1+x)^3} \text {RootSum}\left [1+9 \text {$\#$1}^4+10 \text {$\#$1}^8+3 \text {$\#$1}^{12}\&,\frac {\log \left (\sqrt [4]{-1+x}-\text {$\#$1}\right ) \text {$\#$1}^3}{9+20 \text {$\#$1}^4+9 \text {$\#$1}^8}\&\right ]}{(-1+x)^{3/4}} \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[(-1 + 3*x - 3*x^2 + x^3)^(1/4)/(-1 - 2*x + x^2 + 3*x^3),x]
[Out]
(((-1 + x)^3)^(1/4)*RootSum[1 + 9*#1^4 + 10*#1^8 + 3*#1^12 & , (Log[(-1 + x)^(1/4) - #1]*#1^3)/(9 + 20*#1^4 +
9*#1^8) & ])/(-1 + x)^(3/4)
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fricas [B] time = 1.34, size = 4881, normalized size = 65.96
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x, algorithm="fricas")
[Out]
-2/31*sqrt(31)*sqrt(2)*(2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9
)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^
(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(2246990
3*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(1/4)*arctan
(1/186318941083031826816*sqrt(2)*(sqrt(44939806)*sqrt(1/31)*(1762583*sqrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*s
qrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 + 5662109214*s
qrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 3
89553327)^(1/3) - 1071) + 31*(1762583*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9
)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 1069965*x - 1069965)*sqrt(-3/31*((4/9)^(1/3)*(22469903
*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4
/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1
/3) + 6736019/31) - 39205917*sqrt(31)*(x - 1))*sqrt(2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 38
9553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(224
69903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/
31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327
)^(1/3) - 4284)*sqrt(-((44691*(x^2 - 2*x + 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9
)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 + 54771730*x^2 + 143589951*(x^2 - 2*x + 1)*((4/9)^(1/3
)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 3
*(14897*sqrt(31)*(x^2 - 2*x + 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(2246
9903*sqrt(93) + 389553327)^(1/3) - 1071) + 744*sqrt(31)*(x^2 - 2*x + 1))*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqr
t(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^
(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3)
+ 6736019/31) - 109543460*x + 54771730)*sqrt(2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327
)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*s
qrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2
*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3)
- 4284) - 5572535944*sqrt(x^3 - 3*x^2 + 3*x - 1))/(x^2 - 2*x + 1)) - 89879612*(1762583*sqrt(31)*(x^3 - 3*x^2
+ 3*x - 1)^(1/4)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) +
389553327)^(1/3) - 1071)^2 + 5662109214*sqrt(31)*(x^3 - 3*x^2 + 3*x - 1)^(1/4)*((4/9)^(1/3)*(22469903*sqrt(93)
+ 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 31*sqrt(-3/31*((4/9)^
(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)
^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93)
+ 389553327)^(1/3) + 6736019/31)*(1762583*(x^3 - 3*x^2 + 3*x - 1)^(1/4)*((4/9)^(1/3)*(22469903*sqrt(93) + 3895
53327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 1069965*(x^3 - 3*x^2 + 3*x -
1)^(1/4)) - 39205917*sqrt(31)*(x^3 - 3*x^2 + 3*x - 1)^(1/4))*sqrt(2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(2246990
3*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(
4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(
1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(
93) + 389553327)^(1/3) - 4284))*(2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 61
7793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 38
9553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)
*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(1/
4)/(x - 1)) + 2/31*sqrt(31)*sqrt(2)*(-2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3)
+ 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93)
+ 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^
(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284
)^(1/4)*arctan(-1/186318941083031826816*(sqrt(44939806)*sqrt(2)*sqrt(1/31)*(1762583*sqrt(31)*(x - 1)*((4/9)^(1
/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2
+ 5662109214*sqrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(224699
03*sqrt(93) + 389553327)^(1/3) - 1071) - 31*(1762583*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3
) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 1069965*x - 1069965)*sqrt(-3/31*((4/9)^
(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)
^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93)
+ 389553327)^(1/3) + 6736019/31) - 39205917*sqrt(31)*(x - 1))*(-2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*s
qrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9
)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3
) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93)
+ 389553327)^(1/3) - 4284)^(3/4)*sqrt(-((44691*(x^2 - 2*x + 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(
1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 + 54771730*x^2 + 143589951*(x^2 - 2*
x + 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)
^(1/3) - 1071) - 3*(14897*sqrt(31)*(x^2 - 2*x + 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793
*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 744*sqrt(31)*(x^2 - 2*x + 1))*sqrt(-3/31*((4/9)^(
1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^
2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) +
389553327)^(1/3) + 6736019/31) - 109543460*x + 54771730)*sqrt(-2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*s
qrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9
)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3
) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93)
+ 389553327)^(1/3) - 4284) - 5572535944*sqrt(x^3 - 3*x^2 + 3*x - 1))/(x^2 - 2*x + 1)) - 89879612*sqrt(2)*(176
2583*sqrt(31)*(x^3 - 3*x^2 + 3*x - 1)^(1/4)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^
(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 + 5662109214*sqrt(31)*(x^3 - 3*x^2 + 3*x - 1)^(1/4)*((4/
9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 10
71) - 31*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93)
+ 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9
)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31)*(1762583*(x^3 - 3*x^2 + 3*x - 1)^(1/4)*((4/9)^(1/3
)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 1
069965*(x^3 - 3*x^2 + 3*x - 1)^(1/4)) - 39205917*sqrt(31)*(x^3 - 3*x^2 + 3*x - 1)^(1/4))*(-2*sqrt(31)*sqrt(-3/
31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/
3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903
*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/
9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(3/4))/(x - 1)) - 1/62*sqrt(31)*sqrt(2)*(2*sqrt(31)*sqr
t(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327
)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(224
69903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 123558
6*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(1/4)*log(1/31*(sqrt(2)*(1527*sqrt(31)*(x - 1)*((4
/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1
071)^2 + 5272704*sqrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(224
69903*sqrt(93) + 389553327)^(1/3) - 1071) + 93*(509*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3)
+ 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) - 122151*x + 122151)*sqrt(-3/31*((4/9)^(1/
3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2
- 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 3
89553327)^(1/3) + 6736019/31) + 1076537*sqrt(31)*(x - 1))*(2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(9
3) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/
3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6
736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 38
9553327)^(1/3) - 4284)^(1/4) + 11145071888*(x^3 - 3*x^2 + 3*x - 1)^(1/4))/(x - 1)) + 1/62*sqrt(31)*sqrt(2)*(2*
sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93)
+ 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9
)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1
/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(1/4)*log(-1/31*(sqrt(2)*(1527*sqrt(31
)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 3895533
27)^(1/3) - 1071)^2 + 5272704*sqrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/
9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 93*(509*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389
553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) - 122151*x + 122151)*sqrt(-3/
31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/
3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903
*sqrt(93) + 389553327)^(1/3) + 6736019/31) + 1076537*sqrt(31)*(x - 1))*(2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22
469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426
/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 3895533
27)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*
sqrt(93) + 389553327)^(1/3) - 4284)^(1/4) - 11145071888*(x^3 - 3*x^2 + 3*x - 1)^(1/4))/(x - 1)) - 1/62*sqrt(31
)*sqrt(2)*(-2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(224
69903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969
937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) +
389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(1/4)*log(1/31*(sqrt(2)*
(1527*sqrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(
93) + 389553327)^(1/3) - 1071)^2 + 5272704*sqrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3)
+ 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) - 93*(509*(x - 1)*((4/9)^(1/3)*(22469903*s
qrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) - 122151*x + 122
151)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 3
89553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2
/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) + 1076537*sqrt(31)*(x - 1))*(-2*sqrt(31)*sqrt(-3/31*((
4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) -
1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt
(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2
/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(1/4) + 11145071888*(x^3 - 3*x^2 + 3*x - 1)^(1/4))/(x - 1))
+ 1/62*sqrt(31)*sqrt(2)*(-2*sqrt(31)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4
/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327
)^(1/3) - 3969937818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469
903*sqrt(93) + 389553327)^(1/3) - 1235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(1/4)*log(
-1/31*(sqrt(2)*(1527*sqrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/
(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 + 5272704*sqrt(31)*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 3
89553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) - 93*(509*(x - 1)*((4/9)^(1
/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) -
122151*x + 122151)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(224699
03*sqrt(93) + 389553327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937
818/31*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) + 1076537*sqrt(31)*(x - 1))*(-2*sqrt(31
)*sqrt(-3/31*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 3895
53327)^(1/3) - 1071)^2 - 6426/31*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 3969937818/31*(4/9)^(2/3)
/(22469903*sqrt(93) + 389553327)^(1/3) + 6736019/31) - 2*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) - 1
235586*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 4284)^(1/4) - 11145071888*(x^3 - 3*x^2 + 3*x - 1)^(
1/4))/(x - 1)) + 4*(1/961*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793/961*(4/9)^(2/3)/(22469903
*sqrt(93) + 389553327)^(1/3) - 1071/961)^(1/4)*arctan(1/12117516979905816*(sqrt(44939806)*sqrt(1/31)*(1762583*
(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327
)^(1/3) - 1071)^2 + 5662109214*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)
/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 4611683685803*x - 4611683685803)*(1/961*(4/9)^(1/3)*(22469903
*sqrt(93) + 389553327)^(1/3) + 617793/961*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071/961)^(3/4)*
sqrt(((44691*(x^2 - 2*x + 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903
*sqrt(93) + 389553327)^(1/3) - 1071)^2 + 116943207136*x^2 + 143589951*(x^2 - 2*x + 1)*((4/9)^(1/3)*(22469903*s
qrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) - 233886414272*x
+ 116943207136)*sqrt((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93
) + 389553327)^(1/3) - 1071) + 1393133986*sqrt(x^3 - 3*x^2 + 3*x - 1))/(x^2 - 2*x + 1)) - 44939806*(1762583*(x
^3 - 3*x^2 + 3*x - 1)^(1/4)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*
sqrt(93) + 389553327)^(1/3) - 1071)^2 + 5662109214*(x^3 - 3*x^2 + 3*x - 1)^(1/4)*((4/9)^(1/3)*(22469903*sqrt(9
3) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071) + 4611683685803*(x^3
- 3*x^2 + 3*x - 1)^(1/4))*(1/961*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793/961*(4/9)^(2/3)/(2
2469903*sqrt(93) + 389553327)^(1/3) - 1071/961)^(3/4))/(x - 1)) + (1/961*(4/9)^(1/3)*(22469903*sqrt(93) + 3895
53327)^(1/3) + 617793/961*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071/961)^(1/4)*log(2*((1527*(x
- 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(
1/3) - 1071)^2 + 5272704*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(2246
9903*sqrt(93) + 389553327)^(1/3) - 1071) + 4584936749*x - 4584936749)*(1/961*(4/9)^(1/3)*(22469903*sqrt(93) +
389553327)^(1/3) + 617793/961*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071/961)^(1/4) + 89879612*(
x^3 - 3*x^2 + 3*x - 1)^(1/4))/(x - 1)) - (1/961*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793/961
*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071/961)^(1/4)*log(-2*((1527*(x - 1)*((4/9)^(1/3)*(22469
903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071)^2 + 5272704
*(x - 1)*((4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 617793*(4/9)^(2/3)/(22469903*sqrt(93) + 38955332
7)^(1/3) - 1071) + 4584936749*x - 4584936749)*(1/961*(4/9)^(1/3)*(22469903*sqrt(93) + 389553327)^(1/3) + 61779
3/961*(4/9)^(2/3)/(22469903*sqrt(93) + 389553327)^(1/3) - 1071/961)^(1/4) - 89879612*(x^3 - 3*x^2 + 3*x - 1)^(
1/4))/(x - 1))
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}^{\frac {1}{4}}}{3 \, x^{3} + x^{2} - 2 \, x - 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x, algorithm="giac")
[Out]
integrate((x^3 - 3*x^2 + 3*x - 1)^(1/4)/(3*x^3 + x^2 - 2*x - 1), x)
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maple [F] time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (x^{3}-3 x^{2}+3 x -1\right )^{\frac {1}{4}}}{3 x^{3}+x^{2}-2 x -1}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x)
[Out]
int((x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x)
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}^{\frac {1}{4}}}{3 \, x^{3} + x^{2} - 2 \, x - 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x, algorithm="maxima")
[Out]
integrate((x^3 - 3*x^2 + 3*x - 1)^(1/4)/(3*x^3 + x^2 - 2*x - 1), x)
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} -\int \frac {{\left (x^3-3\,x^2+3\,x-1\right )}^{1/4}}{-3\,x^3-x^2+2\,x+1} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(3*x - 3*x^2 + x^3 - 1)^(1/4)/(2*x - x^2 - 3*x^3 + 1),x)
[Out]
-int((3*x - 3*x^2 + x^3 - 1)^(1/4)/(2*x - x^2 - 3*x^3 + 1), x)
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt [4]{\left (x - 1\right )^{3}}}{3 x^{3} + x^{2} - 2 x - 1}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x**3-3*x**2+3*x-1)**(1/4)/(3*x**3+x**2-2*x-1),x)
[Out]
Integral(((x - 1)**3)**(1/4)/(3*x**3 + x**2 - 2*x - 1), x)
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