3.11.24 \(\int \frac {1}{x^6 \sqrt [6]{a+b x^2}} \, dx\) [1024]

Optimal. Leaf size=661 \[ \frac {8 b^3 x}{27 a^3 \sqrt [6]{a+b x^2}}-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}-\frac {8 b^2 \left (a+b x^2\right )^{5/6}}{27 a^3 x}+\frac {8 b^3 x}{27 a^2 \left (\frac {a}{a+b x^2}\right )^{2/3} \left (a+b x^2\right )^{7/6} \left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )}+\frac {4 \sqrt {2+\sqrt {3}} b^2 \left (1-\sqrt [3]{\frac {a}{a+b x^2}}\right ) \sqrt {\frac {1+\sqrt [3]{\frac {a}{a+b x^2}}+\left (\frac {a}{a+b x^2}\right )^{2/3}}{\left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )^2}} E\left (\sin ^{-1}\left (\frac {1+\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}}{1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}}\right )|-7+4 \sqrt {3}\right )}{9\ 3^{3/4} a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2} \sqrt {-\frac {1-\sqrt [3]{\frac {a}{a+b x^2}}}{\left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )^2}}}-\frac {8 \sqrt {2} b^2 \left (1-\sqrt [3]{\frac {a}{a+b x^2}}\right ) \sqrt {\frac {1+\sqrt [3]{\frac {a}{a+b x^2}}+\left (\frac {a}{a+b x^2}\right )^{2/3}}{\left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )^2}} F\left (\sin ^{-1}\left (\frac {1+\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}}{1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}}\right )|-7+4 \sqrt {3}\right )}{27 \sqrt [4]{3} a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2} \sqrt {-\frac {1-\sqrt [3]{\frac {a}{a+b x^2}}}{\left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )^2}}} \]

[Out]

8/27*b^3*x/a^3/(b*x^2+a)^(1/6)-1/5*(b*x^2+a)^(5/6)/a/x^5+2/9*b*(b*x^2+a)^(5/6)/a^2/x^3-8/27*b^2*(b*x^2+a)^(5/6
)/a^3/x+8/27*b^3*x/a^2/(a/(b*x^2+a))^(2/3)/(b*x^2+a)^(7/6)/(1-(a/(b*x^2+a))^(1/3)-3^(1/2))-8/81*b^2*(1-(a/(b*x
^2+a))^(1/3))*EllipticF((1-(a/(b*x^2+a))^(1/3)+3^(1/2))/(1-(a/(b*x^2+a))^(1/3)-3^(1/2)),2*I-I*3^(1/2))*2^(1/2)
*((1+(a/(b*x^2+a))^(1/3)+(a/(b*x^2+a))^(2/3))/(1-(a/(b*x^2+a))^(1/3)-3^(1/2))^2)^(1/2)*3^(3/4)/a^2/x/(a/(b*x^2
+a))^(2/3)/(b*x^2+a)^(1/6)/((-1+(a/(b*x^2+a))^(1/3))/(1-(a/(b*x^2+a))^(1/3)-3^(1/2))^2)^(1/2)+4/27*b^2*(1-(a/(
b*x^2+a))^(1/3))*EllipticE((1-(a/(b*x^2+a))^(1/3)+3^(1/2))/(1-(a/(b*x^2+a))^(1/3)-3^(1/2)),2*I-I*3^(1/2))*((1+
(a/(b*x^2+a))^(1/3)+(a/(b*x^2+a))^(2/3))/(1-(a/(b*x^2+a))^(1/3)-3^(1/2))^2)^(1/2)*(1/2*6^(1/2)+1/2*2^(1/2))*3^
(1/4)/a^2/x/(a/(b*x^2+a))^(2/3)/(b*x^2+a)^(1/6)/((-1+(a/(b*x^2+a))^(1/3))/(1-(a/(b*x^2+a))^(1/3)-3^(1/2))^2)^(
1/2)

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Rubi [A]
time = 0.47, antiderivative size = 661, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 7, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.467, Rules used = {331, 244, 204, 241, 310, 225, 1893} \begin {gather*} \frac {8 b^3 x}{27 a^3 \sqrt [6]{a+b x^2}}-\frac {8 b^2 \left (a+b x^2\right )^{5/6}}{27 a^3 x}-\frac {8 \sqrt {2} b^2 \left (1-\sqrt [3]{\frac {a}{a+b x^2}}\right ) \sqrt {\frac {\left (\frac {a}{a+b x^2}\right )^{2/3}+\sqrt [3]{\frac {a}{a+b x^2}}+1}{\left (-\sqrt [3]{\frac {a}{a+b x^2}}-\sqrt {3}+1\right )^2}} F\left (\text {ArcSin}\left (\frac {-\sqrt [3]{\frac {a}{b x^2+a}}+\sqrt {3}+1}{-\sqrt [3]{\frac {a}{b x^2+a}}-\sqrt {3}+1}\right )|-7+4 \sqrt {3}\right )}{27 \sqrt [4]{3} a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2} \sqrt {-\frac {1-\sqrt [3]{\frac {a}{a+b x^2}}}{\left (-\sqrt [3]{\frac {a}{a+b x^2}}-\sqrt {3}+1\right )^2}}}+\frac {4 \sqrt {2+\sqrt {3}} b^2 \left (1-\sqrt [3]{\frac {a}{a+b x^2}}\right ) \sqrt {\frac {\left (\frac {a}{a+b x^2}\right )^{2/3}+\sqrt [3]{\frac {a}{a+b x^2}}+1}{\left (-\sqrt [3]{\frac {a}{a+b x^2}}-\sqrt {3}+1\right )^2}} E\left (\text {ArcSin}\left (\frac {-\sqrt [3]{\frac {a}{b x^2+a}}+\sqrt {3}+1}{-\sqrt [3]{\frac {a}{b x^2+a}}-\sqrt {3}+1}\right )|-7+4 \sqrt {3}\right )}{9\ 3^{3/4} a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2} \sqrt {-\frac {1-\sqrt [3]{\frac {a}{a+b x^2}}}{\left (-\sqrt [3]{\frac {a}{a+b x^2}}-\sqrt {3}+1\right )^2}}}+\frac {8 b^3 x}{27 a^2 \left (\frac {a}{a+b x^2}\right )^{2/3} \left (a+b x^2\right )^{7/6} \left (-\sqrt [3]{\frac {a}{a+b x^2}}-\sqrt {3}+1\right )}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1/(x^6*(a + b*x^2)^(1/6)),x]

[Out]

(8*b^3*x)/(27*a^3*(a + b*x^2)^(1/6)) - (a + b*x^2)^(5/6)/(5*a*x^5) + (2*b*(a + b*x^2)^(5/6))/(9*a^2*x^3) - (8*
b^2*(a + b*x^2)^(5/6))/(27*a^3*x) + (8*b^3*x)/(27*a^2*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (
a/(a + b*x^2))^(1/3))) + (4*Sqrt[2 + Sqrt[3]]*b^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3)
+ (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^
2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(3/4)*a^2*x*(a/(a + b*x^2))^(2/3)*(a
+ b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (8*Sqrt[2]*b^2*
(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*
x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))],
-7 + 4*Sqrt[3]])/(27*3^(1/4)*a^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))
/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])

Rule 204

Int[((a_) + (b_.)*(x_)^2)^(-7/6), x_Symbol] :> Dist[1/((a + b*x^2)^(2/3)*(a/(a + b*x^2))^(2/3)), Subst[Int[1/(
1 - b*x^2)^(1/3), x], x, x/Sqrt[a + b*x^2]], x] /; FreeQ[{a, b}, x]

Rule 225

Int[1/Sqrt[(a_) + (b_.)*(x_)^3], x_Symbol] :> With[{r = Numer[Rt[b/a, 3]], s = Denom[Rt[b/a, 3]]}, Simp[2*Sqrt
[2 - Sqrt[3]]*(s + r*x)*(Sqrt[(s^2 - r*s*x + r^2*x^2)/((1 - Sqrt[3])*s + r*x)^2]/(3^(1/4)*r*Sqrt[a + b*x^3]*Sq
rt[(-s)*((s + r*x)/((1 - Sqrt[3])*s + r*x)^2)]))*EllipticF[ArcSin[((1 + Sqrt[3])*s + r*x)/((1 - Sqrt[3])*s + r
*x)], -7 + 4*Sqrt[3]], x]] /; FreeQ[{a, b}, x] && NegQ[a]

Rule 241

Int[((a_) + (b_.)*(x_)^2)^(-1/3), x_Symbol] :> Dist[3*(Sqrt[b*x^2]/(2*b*x)), Subst[Int[x/Sqrt[-a + x^3], x], x
, (a + b*x^2)^(1/3)], x] /; FreeQ[{a, b}, x]

Rule 244

Int[((a_) + (b_.)*(x_)^2)^(-1/6), x_Symbol] :> Simp[3*(x/(2*(a + b*x^2)^(1/6))), x] - Dist[a/2, Int[1/(a + b*x
^2)^(7/6), x], x] /; FreeQ[{a, b}, x]

Rule 310

Int[(x_)/Sqrt[(a_) + (b_.)*(x_)^3], x_Symbol] :> With[{r = Numer[Rt[b/a, 3]], s = Denom[Rt[b/a, 3]]}, Dist[(-(
1 + Sqrt[3]))*(s/r), Int[1/Sqrt[a + b*x^3], x], x] + Dist[1/r, Int[((1 + Sqrt[3])*s + r*x)/Sqrt[a + b*x^3], x]
, x]] /; FreeQ[{a, b}, x] && NegQ[a]

Rule 331

Int[((c_.)*(x_))^(m_)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(c*x)^(m + 1)*((a + b*x^n)^(p + 1)/(a*c
*(m + 1))), x] - Dist[b*((m + n*(p + 1) + 1)/(a*c^n*(m + 1))), Int[(c*x)^(m + n)*(a + b*x^n)^p, x], x] /; Free
Q[{a, b, c, p}, x] && IGtQ[n, 0] && LtQ[m, -1] && IntBinomialQ[a, b, c, n, m, p, x]

Rule 1893

Int[((c_) + (d_.)*(x_))/Sqrt[(a_) + (b_.)*(x_)^3], x_Symbol] :> With[{r = Numer[Simplify[(1 + Sqrt[3])*(d/c)]]
, s = Denom[Simplify[(1 + Sqrt[3])*(d/c)]]}, Simp[2*d*s^3*(Sqrt[a + b*x^3]/(a*r^2*((1 - Sqrt[3])*s + r*x))), x
] + Simp[3^(1/4)*Sqrt[2 + Sqrt[3]]*d*s*(s + r*x)*(Sqrt[(s^2 - r*s*x + r^2*x^2)/((1 - Sqrt[3])*s + r*x)^2]/(r^2
*Sqrt[a + b*x^3]*Sqrt[(-s)*((s + r*x)/((1 - Sqrt[3])*s + r*x)^2)]))*EllipticE[ArcSin[((1 + Sqrt[3])*s + r*x)/(
(1 - Sqrt[3])*s + r*x)], -7 + 4*Sqrt[3]], x]] /; FreeQ[{a, b, c, d}, x] && NegQ[a] && EqQ[b*c^3 - 2*(5 + 3*Sqr
t[3])*a*d^3, 0]

Rubi steps

\begin {align*} \int \frac {1}{x^6 \sqrt [6]{a+b x^2}} \, dx &=-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}-\frac {(2 b) \int \frac {1}{x^4 \sqrt [6]{a+b x^2}} \, dx}{3 a}\\ &=-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}+\frac {\left (8 b^2\right ) \int \frac {1}{x^2 \sqrt [6]{a+b x^2}} \, dx}{27 a^2}\\ &=-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}-\frac {8 b^2 \left (a+b x^2\right )^{5/6}}{27 a^3 x}+\frac {\left (16 b^3\right ) \int \frac {1}{\sqrt [6]{a+b x^2}} \, dx}{81 a^3}\\ &=\frac {8 b^3 x}{27 a^3 \sqrt [6]{a+b x^2}}-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}-\frac {8 b^2 \left (a+b x^2\right )^{5/6}}{27 a^3 x}-\frac {\left (8 b^3\right ) \int \frac {1}{\left (a+b x^2\right )^{7/6}} \, dx}{81 a^2}\\ &=\frac {8 b^3 x}{27 a^3 \sqrt [6]{a+b x^2}}-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}-\frac {8 b^2 \left (a+b x^2\right )^{5/6}}{27 a^3 x}-\frac {\left (8 b^3\right ) \text {Subst}\left (\int \frac {1}{\sqrt [3]{1-b x^2}} \, dx,x,\frac {x}{\sqrt {a+b x^2}}\right )}{81 a^2 \left (\frac {a}{a+b x^2}\right )^{2/3} \left (a+b x^2\right )^{2/3}}\\ &=\frac {8 b^3 x}{27 a^3 \sqrt [6]{a+b x^2}}-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}-\frac {8 b^2 \left (a+b x^2\right )^{5/6}}{27 a^3 x}+\frac {\left (4 b^2 \sqrt {-\frac {b x^2}{a+b x^2}}\right ) \text {Subst}\left (\int \frac {x}{\sqrt {-1+x^3}} \, dx,x,\sqrt [3]{\frac {a}{a+b x^2}}\right )}{27 a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2}}\\ &=\frac {8 b^3 x}{27 a^3 \sqrt [6]{a+b x^2}}-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}-\frac {8 b^2 \left (a+b x^2\right )^{5/6}}{27 a^3 x}-\frac {\left (4 b^2 \sqrt {-\frac {b x^2}{a+b x^2}}\right ) \text {Subst}\left (\int \frac {1+\sqrt {3}-x}{\sqrt {-1+x^3}} \, dx,x,\sqrt [3]{\frac {a}{a+b x^2}}\right )}{27 a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2}}+\frac {\left (4 \sqrt {2 \left (2+\sqrt {3}\right )} b^2 \sqrt {-\frac {b x^2}{a+b x^2}}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {-1+x^3}} \, dx,x,\sqrt [3]{\frac {a}{a+b x^2}}\right )}{27 a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2}}\\ &=\frac {8 b^3 x}{27 a^3 \sqrt [6]{a+b x^2}}-\frac {\left (a+b x^2\right )^{5/6}}{5 a x^5}+\frac {2 b \left (a+b x^2\right )^{5/6}}{9 a^2 x^3}-\frac {8 b^2 \left (a+b x^2\right )^{5/6}}{27 a^3 x}-\frac {8 b^2 \sqrt {-\frac {b x^2}{a+b x^2}} \sqrt {-1+\frac {a}{a+b x^2}}}{27 a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2} \left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )}+\frac {4 \sqrt {2+\sqrt {3}} b^2 \sqrt {-\frac {b x^2}{a+b x^2}} \left (1-\sqrt [3]{\frac {a}{a+b x^2}}\right ) \sqrt {\frac {1+\sqrt [3]{\frac {a}{a+b x^2}}+\left (\frac {a}{a+b x^2}\right )^{2/3}}{\left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )^2}} E\left (\sin ^{-1}\left (\frac {1+\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}}{1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}}\right )|-7+4 \sqrt {3}\right )}{9\ 3^{3/4} a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2} \sqrt {-\frac {1-\sqrt [3]{\frac {a}{a+b x^2}}}{\left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )^2}} \sqrt {-1+\frac {a}{a+b x^2}}}-\frac {8 \sqrt {2} b^2 \sqrt {-\frac {b x^2}{a+b x^2}} \left (1-\sqrt [3]{\frac {a}{a+b x^2}}\right ) \sqrt {\frac {1+\sqrt [3]{\frac {a}{a+b x^2}}+\left (\frac {a}{a+b x^2}\right )^{2/3}}{\left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )^2}} F\left (\sin ^{-1}\left (\frac {1+\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}}{1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}}\right )|-7+4 \sqrt {3}\right )}{27 \sqrt [4]{3} a^2 x \left (\frac {a}{a+b x^2}\right )^{2/3} \sqrt [6]{a+b x^2} \sqrt {-\frac {1-\sqrt [3]{\frac {a}{a+b x^2}}}{\left (1-\sqrt {3}-\sqrt [3]{\frac {a}{a+b x^2}}\right )^2}} \sqrt {-1+\frac {a}{a+b x^2}}}\\ \end {align*}

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Mathematica [C] Result contains higher order function than in optimal. Order 5 vs. order 4 in optimal.
time = 10.01, size = 51, normalized size = 0.08 \begin {gather*} -\frac {\sqrt [6]{1+\frac {b x^2}{a}} \, _2F_1\left (-\frac {5}{2},\frac {1}{6};-\frac {3}{2};-\frac {b x^2}{a}\right )}{5 x^5 \sqrt [6]{a+b x^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1/(x^6*(a + b*x^2)^(1/6)),x]

[Out]

-1/5*((1 + (b*x^2)/a)^(1/6)*Hypergeometric2F1[-5/2, 1/6, -3/2, -((b*x^2)/a)])/(x^5*(a + b*x^2)^(1/6))

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Maple [F]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {1}{x^{6} \left (b \,x^{2}+a \right )^{\frac {1}{6}}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^6/(b*x^2+a)^(1/6),x)

[Out]

int(1/x^6/(b*x^2+a)^(1/6),x)

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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(1/x^6/(b*x^2+a)^(1/6),x, algorithm="maxima")

[Out]

integrate(1/((b*x^2 + a)^(1/6)*x^6), x)

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Fricas [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(1/x^6/(b*x^2+a)^(1/6),x, algorithm="fricas")

[Out]

integral((b*x^2 + a)^(5/6)/(b*x^8 + a*x^6), x)

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Sympy [A]
time = 0.60, size = 32, normalized size = 0.05 \begin {gather*} - \frac {{{}_{2}F_{1}\left (\begin {matrix} - \frac {5}{2}, \frac {1}{6} \\ - \frac {3}{2} \end {matrix}\middle | {\frac {b x^{2} e^{i \pi }}{a}} \right )}}{5 \sqrt [6]{a} x^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**6/(b*x**2+a)**(1/6),x)

[Out]

-hyper((-5/2, 1/6), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(1/6)*x**5)

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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(1/x^6/(b*x^2+a)^(1/6),x, algorithm="giac")

[Out]

integrate(1/((b*x^2 + a)^(1/6)*x^6), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^6*(a + b*x^2)^(1/6)),x)

[Out]

int(1/(x^6*(a + b*x^2)^(1/6)), x)

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