3.24.86 \(\int \frac {1+x}{\sqrt [3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx\)
Optimal. Leaf size=496 \[ -\frac {\log \left (2 x^2+7 x+3\right )}{5 \sqrt [3]{10}}+\frac {\log \left (4 x^4+28 x^3+61 x^2+42 x+9\right )}{10 \sqrt [3]{10}}+\frac {\log \left (2 \sqrt [3]{10} x^3+3 \sqrt [3]{10} x^2+5 \sqrt [3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}-11 \sqrt [3]{10} x-6 \sqrt [3]{10}\right )}{5 \sqrt [3]{10}}-\frac {\log \left (4\ 10^{2/3} x^6+12\ 10^{2/3} x^5-35\ 10^{2/3} x^4-90\ 10^{2/3} x^3+85\ 10^{2/3} x^2+25 \left (8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27\right )^{2/3}+\left (-10 \sqrt [3]{10} x^3-15 \sqrt [3]{10} x^2+55 \sqrt [3]{10} x+30 \sqrt [3]{10}\right ) \sqrt [3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}+132\ 10^{2/3} x+36\ 10^{2/3}\right )}{10 \sqrt [3]{10}}+\frac {\sqrt {3} \tan ^{-1}\left (\frac {5 \sqrt {3} \sqrt [3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}}{-4 \sqrt [3]{10} x^3-6 \sqrt [3]{10} x^2+5 \sqrt [3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}+22 \sqrt [3]{10} x+12 \sqrt [3]{10}}\right )}{5 \sqrt [3]{10}} \]
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Rubi [F] time = 0.34, 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+x}{\sqrt [3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(1 + x)/(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/3),x]
[Out]
((1 + x^2)^(1/3)*(3 + 7*x + 2*x^2)*Defer[Int][(1 + x)/((1 + x^2)^(1/3)*(3 + 7*x + 2*x^2)), x])/((1 + x^2)*(3 +
7*x + 2*x^2)^3)^(1/3)
Rubi steps
\begin {align*} \int \frac {1+x}{\sqrt [3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx &=\int \frac {1+x}{\sqrt [3]{\left (1+x^2\right ) \left (3+7 x+2 x^2\right )^3}} \, dx\\ &=\frac {\left (\sqrt [3]{1+x^2} \left (3+7 x+2 x^2\right )\right ) \int \frac {1+x}{\sqrt [3]{1+x^2} \left (3+7 x+2 x^2\right )} \, dx}{\sqrt [3]{\left (1+x^2\right ) \left (3+7 x+2 x^2\right )^3}}\\ \end {align*}
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Mathematica [F] time = 0.71, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1+x}{\sqrt [3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Integrate[(1 + x)/(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/3),x]
[Out]
Integrate[(1 + x)/(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/3), x]
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IntegrateAlgebraic [A] time = 1.06, size = 496, normalized size = 1.00 \begin {gather*} -\frac {\log \left (2 x^2+7 x+3\right )}{5 \sqrt [3]{10}}+\frac {\log \left (4 x^4+28 x^3+61 x^2+42 x+9\right )}{10 \sqrt [3]{10}}+\frac {\log \left (2 \sqrt [3]{10} x^3+3 \sqrt [3]{10} x^2+5 \sqrt [3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}-11 \sqrt [3]{10} x-6 \sqrt [3]{10}\right )}{5 \sqrt [3]{10}}-\frac {\log \left (4\ 10^{2/3} x^6+12\ 10^{2/3} x^5-35\ 10^{2/3} x^4-90\ 10^{2/3} x^3+85\ 10^{2/3} x^2+25 \left (8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27\right )^{2/3}+\left (-10 \sqrt [3]{10} x^3-15 \sqrt [3]{10} x^2+55 \sqrt [3]{10} x+30 \sqrt [3]{10}\right ) \sqrt [3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}+132\ 10^{2/3} x+36\ 10^{2/3}\right )}{10 \sqrt [3]{10}}+\frac {\sqrt {3} \tan ^{-1}\left (\frac {5 \sqrt {3} \sqrt [3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}}{-4 \sqrt [3]{10} x^3-6 \sqrt [3]{10} x^2+5 \sqrt [3]{8 x^8+84 x^7+338 x^6+679 x^5+825 x^4+784 x^3+522 x^2+189 x+27}+22 \sqrt [3]{10} x+12 \sqrt [3]{10}}\right )}{5 \sqrt [3]{10}} \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[(1 + x)/(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/
3),x]
[Out]
(Sqrt[3]*ArcTan[(5*Sqrt[3]*(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/
3))/(12*10^(1/3) + 22*10^(1/3)*x - 6*10^(1/3)*x^2 - 4*10^(1/3)*x^3 + 5*(27 + 189*x + 522*x^2 + 784*x^3 + 825*x
^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/3))])/(5*10^(1/3)) - Log[3 + 7*x + 2*x^2]/(5*10^(1/3)) + Log[9 + 4
2*x + 61*x^2 + 28*x^3 + 4*x^4]/(10*10^(1/3)) + Log[-6*10^(1/3) - 11*10^(1/3)*x + 3*10^(1/3)*x^2 + 2*10^(1/3)*x
^3 + 5*(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/3)]/(5*10^(1/3)) - L
og[36*10^(2/3) + 132*10^(2/3)*x + 85*10^(2/3)*x^2 - 90*10^(2/3)*x^3 - 35*10^(2/3)*x^4 + 12*10^(2/3)*x^5 + 4*10
^(2/3)*x^6 + (30*10^(1/3) + 55*10^(1/3)*x - 15*10^(1/3)*x^2 - 10*10^(1/3)*x^3)*(27 + 189*x + 522*x^2 + 784*x^3
+ 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8)^(1/3) + 25*(27 + 189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^
5 + 338*x^6 + 84*x^7 + 8*x^8)^(2/3)]/(10*10^(1/3))
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1+x)/(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3),x, algorithm="fricas")
[Out]
Exception raised: TypeError >> Error detected within library code: integrate: implementation incomplete (re
sidue poly has multiple non-linear factors)
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x + 1}{{\left (8 \, x^{8} + 84 \, x^{7} + 338 \, x^{6} + 679 \, x^{5} + 825 \, x^{4} + 784 \, x^{3} + 522 \, x^{2} + 189 \, x + 27\right )}^{\frac {1}{3}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1+x)/(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3),x, algorithm="giac")
[Out]
integrate((x + 1)/(8*x^8 + 84*x^7 + 338*x^6 + 679*x^5 + 825*x^4 + 784*x^3 + 522*x^2 + 189*x + 27)^(1/3), x)
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maple [C] time = 19.66, size = 3644, normalized size = 7.35 \begin {gather*} \text {output too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((1+x)/(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3),x)
[Out]
1/9*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*ln((1279821560256*RootOf(_Z^3-100)^2*(8*x^
8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*x^4-639910780128*RootOf(_Z^3-100)^2*(8*x^8+84
*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*x^3-3555059889600*RootOf(81*RootOf(_Z^3-100)^2+45
0*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*
x+27)^(2/3)-10878483262176*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^
(1/3)*x^2+10238572482048*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1
/3)*x+28069219056600*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*Ro
otOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)-21887249427900*(8*x^8+84*x^7+338*x^6+679*x^5+825
*x^4+784*x^3+522*x^2+189*x+27)^(2/3)-1607334566400*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_
Z^2)*x^7+49877600763600*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^6+384102732164400*Ro
otOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^5+5755429762500*RootOf(81*RootOf(_Z^3-100)^2+4
50*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^5-3549117144375*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*R
ootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^5+17440696250000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z
^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^4-10754900437500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100
)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^4+28777148812500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_
Z^2)^2*RootOf(_Z^3-100)^2*x^3-17745585721875*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*R
ootOf(_Z^3-100)^3*x^3+18208086885000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(
_Z^3-100)^2*x^2-11228116056750*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100
)^3*x^2+3767190390000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x-2
323058494500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x-489933036490
050*RootOf(_Z^3-100)*x^3-565014287032290*RootOf(_Z^3-100)*x^2-389855676546990*RootOf(_Z^3-100)*x-5208684321084
75*RootOf(_Z^3-100)*x^4+144773126687700*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)+374256
25408800*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*RootOf(81*Root
Of(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x-89275137943635*RootOf(_Z^3-100)+632209891249800*RootOf(81*
RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x-236859044099220*RootOf(_Z^3-100)*x^5+139525570000*Root
Of(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^7-86039203500*RootOf(81*Roo
tOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^7+1255730130000*RootOf(81*RootOf(_Z^3-
100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^6-774352831500*RootOf(81*RootOf(_Z^3-100)^2+4
50*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^6+844666871944500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*R
ootOf(_Z^3-100)+2500*_Z^2)*x^4+794500453251000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)
*x^3+916256046655800*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^2-30757294467180*RootOf
(_Z^3-100)*x^6+991171624320*RootOf(_Z^3-100)*x^7+4678203176100*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+5
22*x^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^4+17
77529944800*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+3
38*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(2/3)*x-2339101588050*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+7
84*x^3+522*x^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2
)*x^3-39764726996850*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*Ro
otOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^2+10943624713950*(8*x^8+84*x^7+338*x^6+679*x^5
+825*x^4+784*x^3+522*x^2+189*x+27)^(2/3)*x+7678929361536*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*
x^4+784*x^3+522*x^2+189*x+27)^(1/3))/(1+2*x)^3/(3+x)^4)+1/50*RootOf(_Z^3-100)*ln((-639910780128*RootOf(_Z^3-10
0)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*x^4+319955390064*RootOf(_Z^3-100)^2
*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*x^3+1777529944800*RootOf(81*RootOf(_Z^3
-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+52
2*x^2+189*x+27)^(2/3)+5439241631088*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+1
89*x+27)^(1/3)*x^2-5119286241024*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*
x+27)^(1/3)*x-7295749809300*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*RootOf(_Z^3-
100)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)+21051914292450*(8*x^8+84*x^7+338*x^6+679*
x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(2/3)+7055214687000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)
+2500*_Z^2)*x^7-46719287500500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^6-48048593194
5750*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^5+9858658734375*RootOf(81*RootOf(_Z^3-1
00)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^5-517988678625*RootOf(81*RootOf(_Z^3-100)^2+45
0*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^5+29874723437500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*Roo
tOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^4-1569662662500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^
3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^4+49293293671875*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2
500*_Z^2)^2*RootOf(_Z^3-100)^2*x^3-2589943393125*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^
2)*RootOf(_Z^3-100)^3*x^3+31189211268750*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*Roo
tOf(_Z^3-100)^2*x^2-1638727819650*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-
100)^3*x^2+6452940262500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*
x-339047135100*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x+2488605971
6340*RootOf(_Z^3-100)*x^3+52965943445322*RootOf(_Z^3-100)*x^2+50796041780682*RootOf(_Z^3-100)*x+47766090550005
*RootOf(_Z^3-100)*x^4-247986494287875*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)-97276664
12400*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*RootOf(81*RootOf(
_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x+13029581401893*RootOf(_Z^3-100)-966779510127750*RootOf(81*Roo
tOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x+25245449679546*RootOf(_Z^3-100)*x^5+238997787500*RootOf(8
1*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^7-12557301300*RootOf(81*RootOf(
_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^7+2150980087500*RootOf(81*RootOf(_Z^3-100)
^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^6-113015711700*RootOf(81*RootOf(_Z^3-100)^2+450*_
Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^6-909111733981875*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootO
f(_Z^3-100)+2500*_Z^2)*x^4-473645815267500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^3
-1008078327807750*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^2+2454701258124*RootOf(_Z^
3-100)*x^6-370691534376*RootOf(_Z^3-100)*x^7-1215958301550*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x
^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^4-888764
972400*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^
6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(2/3)*x+607979150775*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3
+522*x^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^3+
10335645563175*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3)*RootOf(_Z^3-100)*RootOf(8
1*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^2-10525957146225*(8*x^8+84*x^7+338*x^6+679*x^5+825*x
^4+784*x^3+522*x^2+189*x+27)^(2/3)*x-3839464680768*RootOf(_Z^3-100)^2*(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+78
4*x^3+522*x^2+189*x+27)^(1/3))/(1+2*x)^3/(3+x)^4)
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x + 1}{{\left (8 \, x^{8} + 84 \, x^{7} + 338 \, x^{6} + 679 \, x^{5} + 825 \, x^{4} + 784 \, x^{3} + 522 \, x^{2} + 189 \, x + 27\right )}^{\frac {1}{3}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1+x)/(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3),x, algorithm="maxima")
[Out]
integrate((x + 1)/(8*x^8 + 84*x^7 + 338*x^6 + 679*x^5 + 825*x^4 + 784*x^3 + 522*x^2 + 189*x + 27)^(1/3), x)
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {x+1}{{\left (8\,x^8+84\,x^7+338\,x^6+679\,x^5+825\,x^4+784\,x^3+522\,x^2+189\,x+27\right )}^{1/3}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((x + 1)/(189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8 + 27)^(1/3),x)
[Out]
int((x + 1)/(189*x + 522*x^2 + 784*x^3 + 825*x^4 + 679*x^5 + 338*x^6 + 84*x^7 + 8*x^8 + 27)^(1/3), x)
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x + 1}{\sqrt [3]{\left (x + 3\right )^{3} \left (2 x + 1\right )^{3} \left (x^{2} + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1+x)/(8*x**8+84*x**7+338*x**6+679*x**5+825*x**4+784*x**3+522*x**2+189*x+27)**(1/3),x)
[Out]
Integral((x + 1)/((x + 3)**3*(2*x + 1)**3*(x**2 + 1))**(1/3), x)
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