∫ 3 √ ________ −6 − 2x + x2

3.20.93 \(\int \frac {\sqrt [3]{-6-2 x+x^2}}{-1+x} \, dx\) [1993]

Optimal. Leaf size=141 \[ \frac {3}{2} \sqrt [3]{-6-2 x+x^2}+\frac {1}{2} \sqrt {3} \sqrt [3]{7} \text {ArcTan}\left (\frac {1}{\sqrt {3}}-\frac {2 \sqrt [3]{-6-2 x+x^2}}{\sqrt {3} \sqrt [3]{7}}\right )-\frac {1}{2} \sqrt [3]{7} \log \left (7+7^{2/3} \sqrt [3]{-6-2 x+x^2}\right )+\frac {1}{4} \sqrt [3]{7} \log \left (-7+7^{2/3} \sqrt [3]{-6-2 x+x^2}-\sqrt [3]{7} \left (-6-2 x+x^2\right )^{2/3}\right ) \]

[Out]

3/2*(x^2-2*x-6)^(1/3)-1/2*3^(1/2)*7^(1/3)*arctan(-1/3*3^(1/2)+2/21*(x^2-2*x-6)^(1/3)*3^(1/2)*7^(2/3))-1/2*7^(1

/3)*ln(7+7^(2/3)*(x^2-2*x-6)^(1/3))+1/4*7^(1/3)*ln(-7+7^(2/3)*(x^2-2*x-6)^(1/3)-7^(1/3)*(x^2-2*x-6)^(2/3))

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Rubi [A]
time = 0.06, antiderivative size = 103, normalized size of antiderivative = 0.73, number of steps used = 7, number of rules used = 7, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.389, Rules used = {708, 272, 52, 60, 631, 210, 31} \begin {gather*} \frac {1}{2} \sqrt {3} \sqrt [3]{7} \text {ArcTan}\left (\frac {\sqrt [3]{7}-2 \sqrt [3]{(x-1)^2-7}}{\sqrt {3} \sqrt [3]{7}}\right )+\frac {3}{2} \sqrt [3]{(x-1)^2-7}-\frac {3}{4} \sqrt [3]{7} \log \left (\sqrt [3]{(x-1)^2-7}+\sqrt [3]{7}\right )+\frac {1}{2} \sqrt [3]{7} \log (1-x) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Int[(-6 - 2*x + x^2)^(1/3)/(-1 + x),x]

[Out]

(3*(-7 + (-1 + x)^2)^(1/3))/2 + (Sqrt[3]*7^(1/3)*ArcTan[(7^(1/3) - 2*(-7 + (-1 + x)^2)^(1/3))/(Sqrt[3]*7^(1/3)

)])/2 - (3*7^(1/3)*Log[7^(1/3) + (-7 + (-1 + x)^2)^(1/3)])/4 + (7^(1/3)*Log[1 - x])/2

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 52

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 60

Int[1/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(2/3)), x_Symbol] :> With[{q = Rt[-(b*c - a*d)/b, 3]}, Simp[-

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 210

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(-(Rt[-a, 2]*Rt[-b, 2])^(-1))*ArcTan[Rt[-b, 2]*(x/Rt[-a, 2])

], x] /; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])

Rule 272

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 631

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 708

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]{-6-2 x+x^2}}{-1+x} \, dx &=\text {Subst}\left (\int \frac {\sqrt [3]{-7+x^2}}{x} \, dx,x,-1+x\right )\\ &=\frac {1}{2} \text {Subst}\left (\int \frac {\sqrt [3]{-7+x}}{x} \, dx,x,(-1+x)^2\right )\\ &=\frac {3}{2} \sqrt [3]{-7+(-1+x)^2}-\frac {7}{2} \text {Subst}\left (\int \frac {1}{(-7+x)^{2/3} x} \, dx,x,(-1+x)^2\right )\\ &=\frac {3}{2} \sqrt [3]{-7+(-1+x)^2}+\frac {1}{2} \sqrt [3]{7} \log (1-x)-\frac {1}{4} \left (3 \sqrt [3]{7}\right ) \text {Subst}\left (\int \frac {1}{\sqrt [3]{7}+x} \, dx,x,\sqrt [3]{-7+(-1+x)^2}\right )-\frac {1}{4} \left (3\ 7^{2/3}\right ) \text {Subst}\left (\int \frac {1}{7^{2/3}-\sqrt [3]{7} x+x^2} \, dx,x,\sqrt [3]{-7+(-1+x)^2}\right )\\ &=\frac {3}{2} \sqrt [3]{-7+(-1+x)^2}-\frac {3}{4} \sqrt [3]{7} \log \left (\sqrt [3]{7}+\sqrt [3]{-7+(-1+x)^2}\right )+\frac {1}{2} \sqrt [3]{7} \log (1-x)-\frac {1}{2} \left (3 \sqrt [3]{7}\right ) \text {Subst}\left (\int \frac {1}{-3-x^2} \, dx,x,1-\frac {2 \sqrt [3]{-7+(-1+x)^2}}{\sqrt [3]{7}}\right )\\ &=\frac {3}{2} \sqrt [3]{-7+(-1+x)^2}+\frac {1}{2} \sqrt {3} \sqrt [3]{7} \tan ^{-1}\left (\frac {7-2\ 7^{2/3} \sqrt [3]{-7+(-1+x)^2}}{7 \sqrt {3}}\right )-\frac {3}{4} \sqrt [3]{7} \log \left (\sqrt [3]{7}+\sqrt [3]{-7+(-1+x)^2}\right )+\frac {1}{2} \sqrt [3]{7} \log (1-x)\\ \end {align*}

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Mathematica [A]
time = 0.20, size = 136, normalized size = 0.96 \begin {gather*} \frac {1}{4} \left (6 \sqrt [3]{-6-2 x+x^2}+2 \sqrt {3} \sqrt [3]{7} \text {ArcTan}\left (\frac {7-2\ 7^{2/3} \sqrt [3]{-6-2 x+x^2}}{7 \sqrt {3}}\right )-2 \sqrt [3]{7} \log \left (7+7^{2/3} \sqrt [3]{-6-2 x+x^2}\right )+\sqrt [3]{7} \log \left (-7+7^{2/3} \sqrt [3]{-6-2 x+x^2}-\sqrt [3]{7} \left (-6-2 x+x^2\right )^{2/3}\right )\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-6 - 2*x + x^2)^(1/3)/(-1 + x),x]

[Out]

(6*(-6 - 2*x + x^2)^(1/3) + 2*Sqrt[3]*7^(1/3)*ArcTan[(7 - 2*7^(2/3)*(-6 - 2*x + x^2)^(1/3))/(7*Sqrt[3])] - 2*7

^(1/3)*Log[7 + 7^(2/3)*(-6 - 2*x + x^2)^(1/3)] + 7^(1/3)*Log[-7 + 7^(2/3)*(-6 - 2*x + x^2)^(1/3) - 7^(1/3)*(-6

- 2*x + x^2)^(2/3)])/4

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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order 3.
time = 5.39, size = 2699, normalized size = 19.14


method	result	size

risch	\(\text {Expression too large to display}\)	\(2699\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((x^2-2*x-6)^(1/3)/(-1+x),x,method=_RETURNVERBOSE)

[Out]

3/2*(x^2-2*x-6)^(1/3)+(1/2*RootOf(_Z^3+7)*ln(-(-1404*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*x^2+2808

*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*x+100548*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z

^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)+15120*(x^4-4*x^3-8*x^2+24*x+36)^(2/3)*RootOf(36*RootOf(_Z

^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^2-5838*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49

*_Z^2)*x^2+13692*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x+16416*RootOf(_Z^3+7)*x^3+95076*Roo

tOf(_Z^3+7)*x^2-222984*RootOf(_Z^3+7)*x+32004*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)-4104*Ro

otOf(_Z^3+7)*x^4-521208*RootOf(_Z^3+7)-16758*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*

RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)*x^2+252*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^4-10

08*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^3+49*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^

3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^4-196*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^

3+7)^2*x^3-98*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^2+1596*RootOf(36*R

ootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^2+588*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf

(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x-9576*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z

^3+7)^3*x-798*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^4+3192*RootOf(36*Roo

tOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^3-100548*(x^4-4*x^3-8*x^2+24*x+36)^(2/3)+8424*R

ootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)+33516*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)

^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)*x)/(x^2-2*x-6)/(-1+x)^2)-1/2*ln((7182*RootOf(_Z^3+7)^2*(x^4-4*

x^3-8*x^2+24*x+36)^(1/3)*x^2-14364*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*x-4914*(x^4-4*x^3-8*x^2+24

*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)+7560*(x^4-4*x^3-8*x^2+24*

x+36)^(2/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^2+64260*RootOf(36*RootOf(_

Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^2-172200*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x+1

7784*RootOf(_Z^3+7)*x^3+52326*RootOf(_Z^3+7)*x^2-140220*RootOf(_Z^3+7)*x-320040*RootOf(36*RootOf(_Z^3+7)^2+42*

_Z*RootOf(_Z^3+7)+49*_Z^2)-4446*RootOf(_Z^3+7)*x^4-260604*RootOf(_Z^3+7)+819*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*R

ootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)*x^2-5460*RootOf(36*RootOf(_Z^3+7)^2+42*

_Z*RootOf(_Z^3+7)+49*_Z^2)*x^4+21840*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^3+490*RootOf(3

6*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^4-1960*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*

RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^3-980*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*

RootOf(_Z^3+7)^2*x^2-798*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^2+5880*Ro

otOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x+4788*RootOf(36*RootOf(_Z^3+7)^2+42

*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x+399*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*Ro

otOf(_Z^3+7)^3*x^4-1596*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^3+4914*(x^

4-4*x^3-8*x^2+24*x+36)^(2/3)-43092*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)-1638*(x^4-4*x^3-8*x^2+24*x

+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)*x)/(x^2-2*x-6)/(-1+x)^2)*Ro

otOf(_Z^3+7)-7/12*ln((7182*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*x^2-14364*RootOf(_Z^3+7)^2*(x^4-4*

x^3-8*x^2+24*x+36)^(1/3)*x-4914*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7

)+49*_Z^2)*RootOf(_Z^3+7)+7560*(x^4-4*x^3-8*x^2+24*x+36)^(2/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)

+49*_Z^2)*RootOf(_Z^3+7)^2+64260*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^2-172200*RootOf(36

*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x+17784*RootOf(_Z^3+7)*x^3+52326*RootOf(_Z^3+7)*x^2-140220*Roo

tOf(_Z^3+7)*x-320040*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)-4446*RootOf(_Z^3+7)*x^4-260604*R

ootOf(_Z^3+7)+819*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*Roo

tOf(_Z^3+7)*x^2-5460*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^4+21840*RootOf(36*RootOf(_Z^3+

7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^3+490*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_

Z^3+7)^2*x^4-1960*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^3-980*RootOf(3

6*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^2-798*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*R

ootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^2+5880*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*Ro

otOf(_Z^3+7)^2*x+4788*RootOf(36*RootOf(_Z^3+7)^...

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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2-2*x-6)^(1/3)/(-1+x),x, algorithm="maxima")

[Out]

integrate((x^2 - 2*x - 6)^(1/3)/(x - 1), x)

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Fricas [A]
time = 0.36, size = 102, normalized size = 0.72 \begin {gather*} \frac {1}{2} \, \sqrt {3} \left (-7\right )^{\frac {1}{3}} \arctan \left (\frac {2}{21} \, \sqrt {3} \left (-7\right )^{\frac {2}{3}} {\left (x^{2} - 2 \, x - 6\right )}^{\frac {1}{3}} - \frac {1}{3} \, \sqrt {3}\right ) - \frac {1}{4} \, \left (-7\right )^{\frac {1}{3}} \log \left (\left (-7\right )^{\frac {2}{3}} + \left (-7\right )^{\frac {1}{3}} {\left (x^{2} - 2 \, x - 6\right )}^{\frac {1}{3}} + {\left (x^{2} - 2 \, x - 6\right )}^{\frac {2}{3}}\right ) + \frac {1}{2} \, \left (-7\right )^{\frac {1}{3}} \log \left (-\left (-7\right )^{\frac {1}{3}} + {\left (x^{2} - 2 \, x - 6\right )}^{\frac {1}{3}}\right ) + \frac {3}{2} \, {\left (x^{2} - 2 \, x - 6\right )}^{\frac {1}{3}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2-2*x-6)^(1/3)/(-1+x),x, algorithm="fricas")

[Out]

1/2*sqrt(3)*(-7)^(1/3)*arctan(2/21*sqrt(3)*(-7)^(2/3)*(x^2 - 2*x - 6)^(1/3) - 1/3*sqrt(3)) - 1/4*(-7)^(1/3)*lo

g((-7)^(2/3) + (-7)^(1/3)*(x^2 - 2*x - 6)^(1/3) + (x^2 - 2*x - 6)^(2/3)) + 1/2*(-7)^(1/3)*log(-(-7)^(1/3) + (x

^2 - 2*x - 6)^(1/3)) + 3/2*(x^2 - 2*x - 6)^(1/3)

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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt [3]{x^{2} - 2 x - 6}}{x - 1}\, dx \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((x**2-2*x-6)**(1/3)/(-1+x),x)

[Out]

Integral((x**2 - 2*x - 6)**(1/3)/(x - 1), x)

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2-2*x-6)^(1/3)/(-1+x),x, algorithm="giac")

[Out]

integrate((x^2 - 2*x - 6)^(1/3)/(x - 1), x)

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Mupad [F]
time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {{\left (x^2-2\,x-6\right )}^{1/3}}{x-1} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((x^2 - 2*x - 6)^(1/3)/(x - 1),x)

[Out]

int((x^2 - 2*x - 6)^(1/3)/(x - 1), x)

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