3.19.76 \(\int \frac {\sqrt [3]{-1-2 x+6 x^2}}{-1+6 x} \, dx\)
Optimal. Leaf size=174 \[ \frac {1}{4} \sqrt [3]{6 x^2-2 x-1}-\frac {1}{12} \sqrt [3]{\frac {7}{6}} \log \left (\sqrt [3]{6} 7^{2/3} \sqrt [3]{6 x^2-2 x-1}+7\right )+\frac {1}{24} \sqrt [3]{\frac {7}{6}} \log \left (6^{2/3} \sqrt [3]{7} \left (6 x^2-2 x-1\right )^{2/3}-\sqrt [3]{6} 7^{2/3} \sqrt [3]{6 x^2-2 x-1}+7\right )+\frac {\sqrt [3]{\frac {7}{2}} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\frac {2 \sqrt [3]{\frac {2}{7}} \sqrt [3]{6 x^2-2 x-1}}{\sqrt [6]{3}}\right )}{4\ 3^{5/6}} \]
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Rubi [A] time = 0.16, antiderivative size = 119, normalized size of antiderivative = 0.68,
number of steps used = 7, number of rules used = 7, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.318, Rules used =
{694, 266, 50, 58, 617, 204, 31} \begin {gather*} \frac {\sqrt [3]{(6 x-1)^2-7}}{4 \sqrt [3]{6}}+\frac {1}{12} \sqrt [3]{\frac {7}{6}} \log (1-6 x)-\frac {1}{8} \sqrt [3]{\frac {7}{6}} \log \left (\sqrt [3]{(6 x-1)^2-7}+\sqrt [3]{7}\right )+\frac {\sqrt [3]{\frac {7}{2}} \tan ^{-1}\left (\frac {7-2\ 7^{2/3} \sqrt [3]{(6 x-1)^2-7}}{7 \sqrt {3}}\right )}{4\ 3^{5/6}} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(-1 - 2*x + 6*x^2)^(1/3)/(-1 + 6*x),x]
[Out]
(-7 + (-1 + 6*x)^2)^(1/3)/(4*6^(1/3)) + ((7/2)^(1/3)*ArcTan[(7 - 2*7^(2/3)*(-7 + (-1 + 6*x)^2)^(1/3))/(7*Sqrt[
3])])/(4*3^(5/6)) + ((7/6)^(1/3)*Log[1 - 6*x])/12 - ((7/6)^(1/3)*Log[7^(1/3) + (-7 + (-1 + 6*x)^2)^(1/3)])/8
Rule 31
Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]
Rule 50
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^n)/(b*
(m + n + 1)), x] + Dist[(n*(b*c - a*d))/(b*(m + n + 1)), Int[(a + b*x)^m*(c + d*x)^(n - 1), x], x] /; FreeQ[{a
, b, c, d}, x] && NeQ[b*c - a*d, 0] && GtQ[n, 0] && NeQ[m + n + 1, 0] && !(IGtQ[m, 0] && ( !IntegerQ[n] || (G
tQ[m, 0] && LtQ[m - n, 0]))) && !ILtQ[m + n + 2, 0] && IntLinearQ[a, b, c, d, m, n, x]
Rule 58
Int[1/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(2/3)), x_Symbol] :> With[{q = Rt[-((b*c - a*d)/b), 3]}, -Sim
p[Log[RemoveContent[a + b*x, x]]/(2*b*q^2), x] + (Dist[3/(2*b*q), Subst[Int[1/(q^2 - q*x + x^2), x], x, (c + d
*x)^(1/3)], x] + Dist[3/(2*b*q^2), Subst[Int[1/(q + x), x], x, (c + d*x)^(1/3)], x])] /; FreeQ[{a, b, c, d}, x
] && NegQ[(b*c - a*d)/b]
Rule 204
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /
; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])
Rule 266
Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Dist[1/n, Subst[Int[x^(Simplify[(m + 1)/n] - 1)*(a
+ b*x)^p, x], x, x^n], x] /; FreeQ[{a, b, m, n, p}, x] && IntegerQ[Simplify[(m + 1)/n]]
Rule 617
Int[((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> With[{q = 1 - 4*Simplify[(a*c)/b^2]}, Dist[-2/b, Sub
st[Int[1/(q - x^2), x], x, 1 + (2*c*x)/b], x] /; RationalQ[q] && (EqQ[q^2, 1] || !RationalQ[b^2 - 4*a*c])] /;
FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]
Rule 694
Int[((d_) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Dist[1/e, Subst[Int[x^m*(
a - b^2/(4*c) + (c*x^2)/e^2)^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, m, p}, x] && NeQ[b^2 - 4*a*c, 0]
&& EqQ[2*c*d - b*e, 0]
Rubi steps
\begin {align*} \int \frac {\sqrt [3]{-1-2 x+6 x^2}}{-1+6 x} \, dx &=\frac {1}{6} \operatorname {Subst}\left (\int \frac {\sqrt [3]{-\frac {7}{6}+\frac {x^2}{6}}}{x} \, dx,x,-1+6 x\right )\\ &=\frac {1}{12} \operatorname {Subst}\left (\int \frac {\sqrt [3]{-\frac {7}{6}+\frac {x}{6}}}{x} \, dx,x,(-1+6 x)^2\right )\\ &=\frac {\sqrt [3]{-7+(-1+6 x)^2}}{4 \sqrt [3]{6}}-\frac {7}{72} \operatorname {Subst}\left (\int \frac {1}{\left (-\frac {7}{6}+\frac {x}{6}\right )^{2/3} x} \, dx,x,(-1+6 x)^2\right )\\ &=\frac {\sqrt [3]{-7+(-1+6 x)^2}}{4 \sqrt [3]{6}}+\frac {1}{12} \sqrt [3]{\frac {7}{6}} \log (1-6 x)-\frac {1}{8} \sqrt [3]{\frac {7}{6}} \operatorname {Subst}\left (\int \frac {1}{\sqrt [3]{\frac {7}{6}}+x} \, dx,x,\sqrt [3]{-1-2 x+6 x^2}\right )-\frac {1}{8} \left (\frac {7}{6}\right )^{2/3} \operatorname {Subst}\left (\int \frac {1}{\left (\frac {7}{6}\right )^{2/3}-\sqrt [3]{\frac {7}{6}} x+x^2} \, dx,x,\sqrt [3]{-1-2 x+6 x^2}\right )\\ &=\frac {\sqrt [3]{-7+(-1+6 x)^2}}{4 \sqrt [3]{6}}+\frac {1}{12} \sqrt [3]{\frac {7}{6}} \log (1-6 x)-\frac {1}{8} \sqrt [3]{\frac {7}{6}} \log \left (\sqrt [3]{7}+\sqrt [3]{6} \sqrt [3]{-1-2 x+6 x^2}\right )-\frac {1}{4} \sqrt [3]{\frac {7}{6}} \operatorname {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,1-2 \sqrt [3]{\frac {6}{7}} \sqrt [3]{-1-2 x+6 x^2}\right )\\ &=\frac {\sqrt [3]{-7+(-1+6 x)^2}}{4 \sqrt [3]{6}}+\frac {\sqrt [3]{\frac {7}{2}} \tan ^{-1}\left (\frac {7-2 \sqrt [3]{6} 7^{2/3} \sqrt [3]{-1-2 x+6 x^2}}{7 \sqrt {3}}\right )}{4\ 3^{5/6}}+\frac {1}{12} \sqrt [3]{\frac {7}{6}} \log (1-6 x)-\frac {1}{8} \sqrt [3]{\frac {7}{6}} \log \left (\sqrt [3]{7}+\sqrt [3]{6} \sqrt [3]{-1-2 x+6 x^2}\right )\\ \end {align*}
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Mathematica [A] time = 0.12, size = 152, normalized size = 0.87 \begin {gather*} \frac {1}{4} \sqrt [3]{6 x^2-2 x-1}+\frac {\sqrt [3]{\frac {7}{2}} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\frac {2 \sqrt [3]{\frac {2}{7}} \sqrt [3]{6 x^2-2 x-1}}{\sqrt [6]{3}}\right )}{4\ 3^{5/6}}-\frac {1}{12} \sqrt [3]{\frac {7}{6}} \log \left (\sqrt [3]{(1-6 x)^2-7}+\sqrt [3]{7}\right )+\frac {1}{24} \sqrt [3]{\frac {7}{6}} \log \left (\left ((1-6 x)^2-7\right )^{2/3}-\sqrt [3]{7} \sqrt [3]{(1-6 x)^2-7}+7^{2/3}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-1 - 2*x + 6*x^2)^(1/3)/(-1 + 6*x),x]
[Out]
(-1 - 2*x + 6*x^2)^(1/3)/4 + ((7/2)^(1/3)*ArcTan[1/Sqrt[3] - (2*(2/7)^(1/3)*(-1 - 2*x + 6*x^2)^(1/3))/3^(1/6)]
)/(4*3^(5/6)) - ((7/6)^(1/3)*Log[7^(1/3) + (-7 + (1 - 6*x)^2)^(1/3)])/12 + ((7/6)^(1/3)*Log[7^(2/3) - 7^(1/3)*
(-7 + (1 - 6*x)^2)^(1/3) + (-7 + (1 - 6*x)^2)^(2/3)])/24
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IntegrateAlgebraic [A] time = 0.44, size = 174, normalized size = 1.00 \begin {gather*} \frac {1}{4} \sqrt [3]{6 x^2-2 x-1}-\frac {1}{12} \sqrt [3]{\frac {7}{6}} \log \left (\sqrt [3]{6} 7^{2/3} \sqrt [3]{6 x^2-2 x-1}+7\right )+\frac {1}{24} \sqrt [3]{\frac {7}{6}} \log \left (6^{2/3} \sqrt [3]{7} \left (6 x^2-2 x-1\right )^{2/3}-\sqrt [3]{6} 7^{2/3} \sqrt [3]{6 x^2-2 x-1}+7\right )+\frac {\sqrt [3]{\frac {7}{2}} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\frac {2 \sqrt [3]{\frac {2}{7}} \sqrt [3]{6 x^2-2 x-1}}{\sqrt [6]{3}}\right )}{4\ 3^{5/6}} \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[(-1 - 2*x + 6*x^2)^(1/3)/(-1 + 6*x),x]
[Out]
(-1 - 2*x + 6*x^2)^(1/3)/4 + ((7/2)^(1/3)*ArcTan[1/Sqrt[3] - (2*(2/7)^(1/3)*(-1 - 2*x + 6*x^2)^(1/3))/3^(1/6)]
)/(4*3^(5/6)) - ((7/6)^(1/3)*Log[7 + 6^(1/3)*7^(2/3)*(-1 - 2*x + 6*x^2)^(1/3)])/12 + ((7/6)^(1/3)*Log[7 - 6^(1
/3)*7^(2/3)*(-1 - 2*x + 6*x^2)^(1/3) + 6^(2/3)*7^(1/3)*(-1 - 2*x + 6*x^2)^(2/3)])/24
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fricas [A] time = 0.84, size = 146, normalized size = 0.84 \begin {gather*} \frac {1}{24} \cdot 6^{\frac {1}{6}} \sqrt {2} \left (-7\right )^{\frac {1}{3}} \arctan \left (\frac {1}{42} \cdot 6^{\frac {1}{6}} {\left (2 \cdot 6^{\frac {2}{3}} \sqrt {2} \left (-7\right )^{\frac {2}{3}} {\left (6 \, x^{2} - 2 \, x - 1\right )}^{\frac {1}{3}} - 7 \cdot 6^{\frac {1}{3}} \sqrt {2}\right )}\right ) - \frac {1}{144} \cdot 6^{\frac {2}{3}} \left (-7\right )^{\frac {1}{3}} \log \left (6^{\frac {2}{3}} \left (-7\right )^{\frac {1}{3}} {\left (6 \, x^{2} - 2 \, x - 1\right )}^{\frac {1}{3}} + 6^{\frac {1}{3}} \left (-7\right )^{\frac {2}{3}} + 6 \, {\left (6 \, x^{2} - 2 \, x - 1\right )}^{\frac {2}{3}}\right ) + \frac {1}{72} \cdot 6^{\frac {2}{3}} \left (-7\right )^{\frac {1}{3}} \log \left (-6^{\frac {2}{3}} \left (-7\right )^{\frac {1}{3}} + 6 \, {\left (6 \, x^{2} - 2 \, x - 1\right )}^{\frac {1}{3}}\right ) + \frac {1}{4} \, {\left (6 \, x^{2} - 2 \, x - 1\right )}^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((6*x^2-2*x-1)^(1/3)/(-1+6*x),x, algorithm="fricas")
[Out]
1/24*6^(1/6)*sqrt(2)*(-7)^(1/3)*arctan(1/42*6^(1/6)*(2*6^(2/3)*sqrt(2)*(-7)^(2/3)*(6*x^2 - 2*x - 1)^(1/3) - 7*
6^(1/3)*sqrt(2))) - 1/144*6^(2/3)*(-7)^(1/3)*log(6^(2/3)*(-7)^(1/3)*(6*x^2 - 2*x - 1)^(1/3) + 6^(1/3)*(-7)^(2/
3) + 6*(6*x^2 - 2*x - 1)^(2/3)) + 1/72*6^(2/3)*(-7)^(1/3)*log(-6^(2/3)*(-7)^(1/3) + 6*(6*x^2 - 2*x - 1)^(1/3))
+ 1/4*(6*x^2 - 2*x - 1)^(1/3)
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (6 \, x^{2} - 2 \, x - 1\right )}^{\frac {1}{3}}}{6 \, x - 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((6*x^2-2*x-1)^(1/3)/(-1+6*x),x, algorithm="giac")
[Out]
integrate((6*x^2 - 2*x - 1)^(1/3)/(6*x - 1), x)
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maple [C] time = 8.25, size = 2661, normalized size = 15.29 \begin {gather*} \text {Expression too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((6*x^2-2*x-1)^(1/3)/(-1+6*x),x)
[Out]
1/4*(6*x^2-2*x-1)^(1/3)+(1/72*RootOf(_Z^3+252)*ln(-(15846*RootOf(_Z^3+252)*x^2-6194*RootOf(_Z^3+252)*x-2413*Ro
otOf(_Z^3+252)+5334*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)-35028*RootOf(RootOf(_Z^3+252)^
2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x^2+13692*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x+54
432*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x^4-36288*RootOf(RootOf(_Z^3+252)^2+42*_Z*Root
Of(_Z^3+252)+1764*_Z^2)*x^3-24624*RootOf(_Z^3+252)*x^4+16416*RootOf(_Z^3+252)*x^3-100548*(36*x^4-24*x^3-8*x^2+
4*x+1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)*x^2+10584*RootOf(Roo
tOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x^4-7056*RootOf(RootOf(_Z^3+252)^2+42*_
Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x^3-4788*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1
764*_Z^2)*RootOf(_Z^3+252)^3*x^4+3192*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+
252)^3*x^3-588*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x^2+266*RootOf
(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)^3*x^2+588*RootOf(RootOf(_Z^3+252)^2+42*
_Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x-266*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+176
4*_Z^2)*RootOf(_Z^3+252)^3*x+39*RootOf(_Z^3+252)^2*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)+33516*(36*x^4-24*x^3-8*x^
2+4*x+1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)*x-16758*(36*x^4-24
*x^3-8*x^2+4*x+1)^(2/3)+2520*(36*x^4-24*x^3-8*x^2+4*x+1)^(2/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252
)+1764*_Z^2)*RootOf(_Z^3+252)^2-234*RootOf(_Z^3+252)^2*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*x^2+78*RootOf(_Z^3+25
2)^2*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*x+16758*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+42*
_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252))/(6*x^2-2*x-1)/(-1+6*x)^2)-1/72*ln((17442*RootOf(_Z^3+252)*x^2
-7790*RootOf(_Z^3+252)*x-2413*RootOf(_Z^3+252)-106680*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z
^2)+771120*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x^2-344400*RootOf(RootOf(_Z^3+252)^2+42
*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x-2358720*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x^4+1572
480*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x^3-53352*RootOf(_Z^3+252)*x^4+35568*RootOf(_Z
^3+252)*x^3+9828*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)
*RootOf(_Z^3+252)*x^2+211680*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*
x^4-141120*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x^3+4788*RootOf(Ro
otOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)^3*x^4-3192*RootOf(RootOf(_Z^3+252)^2+42*_Z
*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)^3*x^3-11760*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+176
4*_Z^2)^2*RootOf(_Z^3+252)^2*x^2-266*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+2
52)^3*x^2+11760*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x+266*RootOf(
RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)^3*x-399*RootOf(_Z^3+252)^2*(36*x^4-24*x^
3-8*x^2+4*x+1)^(1/3)-3276*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1
764*_Z^2)*RootOf(_Z^3+252)*x+1638*(36*x^4-24*x^3-8*x^2+4*x+1)^(2/3)+2520*(36*x^4-24*x^3-8*x^2+4*x+1)^(2/3)*Roo
tOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)^2+2394*RootOf(_Z^3+252)^2*(36*x^4-24
*x^3-8*x^2+4*x+1)^(1/3)*x^2-798*RootOf(_Z^3+252)^2*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*x-1638*(36*x^4-24*x^3-8*x
^2+4*x+1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252))/(6*x^2-2*x-1)/(-
1+6*x)^2)*RootOf(_Z^3+252)-7/12*ln((17442*RootOf(_Z^3+252)*x^2-7790*RootOf(_Z^3+252)*x-2413*RootOf(_Z^3+252)-1
06680*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)+771120*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootO
f(_Z^3+252)+1764*_Z^2)*x^2-344400*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x-2358720*RootOf
(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*x^4+1572480*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+
252)+1764*_Z^2)*x^3-53352*RootOf(_Z^3+252)*x^4+35568*RootOf(_Z^3+252)*x^3+9828*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/
3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)*x^2+211680*RootOf(RootOf(_Z^3+
252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x^4-141120*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootO
f(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x^3+4788*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^
2)*RootOf(_Z^3+252)^3*x^4-3192*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)^3*
x^3-11760*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x^2-266*RootOf(Root
Of(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)^3*x^2+11760*RootOf(RootOf(_Z^3+252)^2+42*_Z*
RootOf(_Z^3+252)+1764*_Z^2)^2*RootOf(_Z^3+252)^2*x+266*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_
Z^2)*RootOf(_Z^3+252)^3*x-399*RootOf(_Z^3+252)^2*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)-3276*(36*x^4-24*x^3-8*x^2+4
*x+1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252)*x+1638*(36*x^4-24*x^3
-8*x^2+4*x+1)^(2/3)+2520*(36*x^4-24*x^3-8*x^2+4*x+1)^(2/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf(_Z^3+252)+17
64*_Z^2)*RootOf(_Z^3+252)^2+2394*RootOf(_Z^3+252)^2*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*x^2-798*RootOf(_Z^3+252)
^2*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*x-1638*(36*x^4-24*x^3-8*x^2+4*x+1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+42*_Z*
RootOf(_Z^3+252)+1764*_Z^2)*RootOf(_Z^3+252))/(6*x^2-2*x-1)/(-1+6*x)^2)*RootOf(RootOf(_Z^3+252)^2+42*_Z*RootOf
(_Z^3+252)+1764*_Z^2))/(6*x^2-2*x-1)^(2/3)*((6*x^2-2*x-1)^2)^(1/3)
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (6 \, x^{2} - 2 \, x - 1\right )}^{\frac {1}{3}}}{6 \, x - 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((6*x^2-2*x-1)^(1/3)/(-1+6*x),x, algorithm="maxima")
[Out]
integrate((6*x^2 - 2*x - 1)^(1/3)/(6*x - 1), x)
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {{\left (6\,x^2-2\,x-1\right )}^{1/3}}{6\,x-1} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((6*x^2 - 2*x - 1)^(1/3)/(6*x - 1),x)
[Out]
int((6*x^2 - 2*x - 1)^(1/3)/(6*x - 1), x)
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt [3]{6 x^{2} - 2 x - 1}}{6 x - 1}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((6*x**2-2*x-1)**(1/3)/(-1+6*x),x)
[Out]
Integral((6*x**2 - 2*x - 1)**(1/3)/(6*x - 1), x)
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