3.340 \(\int \frac {1}{(a-i b \sin ^{-1}(1+i d x^2))^{5/2}} \, dx\)

Optimal. Leaf size=326 \[ -\frac {\sqrt {\pi } \sqrt {-i b} x \left (\sinh \left (\frac {a}{2 b}\right )+i \cosh \left (\frac {a}{2 b}\right )\right ) C\left (\frac {\sqrt {a-i b \sin ^{-1}\left (i d x^2+1\right )}}{\sqrt {-i b} \sqrt {\pi }}\right )}{3 b^3 \left (\cos \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )-\sin \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )\right )}-\frac {\sqrt {\pi } x \left (\cosh \left (\frac {a}{2 b}\right )+i \sinh \left (\frac {a}{2 b}\right )\right ) S\left (\frac {\sqrt {a-i b \sin ^{-1}\left (i d x^2+1\right )}}{\sqrt {-i b} \sqrt {\pi }}\right )}{3 \sqrt {-i b} b^2 \left (\cos \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )-\sin \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )\right )}-\frac {x}{3 b^2 \sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}}-\frac {\sqrt {d^2 x^4-2 i d x^2}}{3 b d x \left (a-i b \sin ^{-1}\left (1+i d x^2\right )\right )^{3/2}} \]

[Out]

-1/3*x*FresnelS((a-I*b*arcsin(1+I*d*x^2))^(1/2)/(-I*b)^(1/2)/Pi^(1/2))*(cosh(1/2*a/b)+I*sinh(1/2*a/b))*Pi^(1/2
)/b^2/(cos(1/2*arcsin(1+I*d*x^2))-sin(1/2*arcsin(1+I*d*x^2)))/(-I*b)^(1/2)-1/3*x*FresnelC((a-I*b*arcsin(1+I*d*
x^2))^(1/2)/(-I*b)^(1/2)/Pi^(1/2))*(I*cosh(1/2*a/b)+sinh(1/2*a/b))*(-I*b)^(1/2)*Pi^(1/2)/b^3/(cos(1/2*arcsin(1
+I*d*x^2))-sin(1/2*arcsin(1+I*d*x^2)))-1/3*(-2*I*d*x^2+d^2*x^4)^(1/2)/b/d/x/(a-I*b*arcsin(1+I*d*x^2))^(3/2)-1/
3*x/b^2/(a-I*b*arcsin(1+I*d*x^2))^(1/2)

________________________________________________________________________________________

Rubi [A]  time = 0.07, antiderivative size = 326, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {4828, 4819} \[ -\frac {\sqrt {\pi } \sqrt {-i b} x \left (\sinh \left (\frac {a}{2 b}\right )+i \cosh \left (\frac {a}{2 b}\right )\right ) \text {FresnelC}\left (\frac {\sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}}{\sqrt {\pi } \sqrt {-i b}}\right )}{3 b^3 \left (\cos \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )-\sin \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )\right )}-\frac {\sqrt {\pi } x \left (\cosh \left (\frac {a}{2 b}\right )+i \sinh \left (\frac {a}{2 b}\right )\right ) S\left (\frac {\sqrt {a-i b \sin ^{-1}\left (i d x^2+1\right )}}{\sqrt {-i b} \sqrt {\pi }}\right )}{3 \sqrt {-i b} b^2 \left (\cos \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )-\sin \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )\right )}-\frac {x}{3 b^2 \sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}}-\frac {\sqrt {d^2 x^4-2 i d x^2}}{3 b d x \left (a-i b \sin ^{-1}\left (1+i d x^2\right )\right )^{3/2}} \]

Antiderivative was successfully verified.

[In]

Int[(a - I*b*ArcSin[1 + I*d*x^2])^(-5/2),x]

[Out]

-Sqrt[(-2*I)*d*x^2 + d^2*x^4]/(3*b*d*x*(a - I*b*ArcSin[1 + I*d*x^2])^(3/2)) - x/(3*b^2*Sqrt[a - I*b*ArcSin[1 +
I*d*x^2]]) - (Sqrt[Pi]*x*FresnelS[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] +
I*Sinh[a/(2*b)]))/(3*Sqrt[(-I)*b]*b^2*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) - (Sqrt[(-I)
*b]*Sqrt[Pi]*x*FresnelC[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(I*Cosh[a/(2*b)] + Sinh[a/(
2*b)]))/(3*b^3*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))

Rule 4819

Int[1/Sqrt[(a_.) + ArcSin[(c_) + (d_.)*(x_)^2]*(b_.)], x_Symbol] :> -Simp[(Sqrt[Pi]*x*(Cos[a/(2*b)] - c*Sin[a/
(2*b)])*FresnelC[(1*Sqrt[a + b*ArcSin[c + d*x^2]])/(Sqrt[b*c]*Sqrt[Pi])])/(Sqrt[b*c]*(Cos[ArcSin[c + d*x^2]/2]
- c*Sin[ArcSin[c + d*x^2]/2])), x] - Simp[(Sqrt[Pi]*x*(Cos[a/(2*b)] + c*Sin[a/(2*b)])*FresnelS[(1/(Sqrt[b*c]*
Sqrt[Pi]))*Sqrt[a + b*ArcSin[c + d*x^2]]])/(Sqrt[b*c]*(Cos[ArcSin[c + d*x^2]/2] - c*Sin[ArcSin[c + d*x^2]/2]))
, x] /; FreeQ[{a, b, c, d}, x] && EqQ[c^2, 1]

Rule 4828

Int[((a_.) + ArcSin[(c_) + (d_.)*(x_)^2]*(b_.))^(n_), x_Symbol] :> Simp[(x*(a + b*ArcSin[c + d*x^2])^(n + 2))/
(4*b^2*(n + 1)*(n + 2)), x] + (-Dist[1/(4*b^2*(n + 1)*(n + 2)), Int[(a + b*ArcSin[c + d*x^2])^(n + 2), x], x]
+ Simp[(Sqrt[-2*c*d*x^2 - d^2*x^4]*(a + b*ArcSin[c + d*x^2])^(n + 1))/(2*b*d*(n + 1)*x), x]) /; FreeQ[{a, b, c
, d}, x] && EqQ[c^2, 1] && LtQ[n, -1] && NeQ[n, -2]

Rubi steps

\begin {align*} \int \frac {1}{\left (a-i b \sin ^{-1}\left (1+i d x^2\right )\right )^{5/2}} \, dx &=-\frac {\sqrt {-2 i d x^2+d^2 x^4}}{3 b d x \left (a-i b \sin ^{-1}\left (1+i d x^2\right )\right )^{3/2}}-\frac {x}{3 b^2 \sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}}+\frac {\int \frac {1}{\sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}} \, dx}{3 b^2}\\ &=-\frac {\sqrt {-2 i d x^2+d^2 x^4}}{3 b d x \left (a-i b \sin ^{-1}\left (1+i d x^2\right )\right )^{3/2}}-\frac {x}{3 b^2 \sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}}-\frac {\sqrt {\pi } x S\left (\frac {\sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}}{\sqrt {-i b} \sqrt {\pi }}\right ) \left (\cosh \left (\frac {a}{2 b}\right )+i \sinh \left (\frac {a}{2 b}\right )\right )}{3 \sqrt {-i b} b^2 \left (\cos \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )-\sin \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )\right )}-\frac {\sqrt {-i b} \sqrt {\pi } x C\left (\frac {\sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}}{\sqrt {-i b} \sqrt {\pi }}\right ) \left (i \cosh \left (\frac {a}{2 b}\right )+\sinh \left (\frac {a}{2 b}\right )\right )}{3 b^3 \left (\cos \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )-\sin \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )\right )}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.85, size = 308, normalized size = 0.94 \[ -\frac {\frac {\sqrt {\pi } x \left (\cosh \left (\frac {a}{2 b}\right )-i \sinh \left (\frac {a}{2 b}\right )\right ) C\left (\frac {\sqrt {a-i b \sin ^{-1}\left (i d x^2+1\right )}}{\sqrt {-i b} \sqrt {\pi }}\right )}{\sqrt {-i b} \left (\cos \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )-\sin \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )\right )}+\frac {\sqrt {\pi } x \left (\cosh \left (\frac {a}{2 b}\right )+i \sinh \left (\frac {a}{2 b}\right )\right ) S\left (\frac {\sqrt {a-i b \sin ^{-1}\left (i d x^2+1\right )}}{\sqrt {-i b} \sqrt {\pi }}\right )}{\sqrt {-i b} \left (\cos \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )-\sin \left (\frac {1}{2} \sin ^{-1}\left (1+i d x^2\right )\right )\right )}+\frac {b \sqrt {d x^2 \left (d x^2-2 i\right )}}{d x \left (a-i b \sin ^{-1}\left (1+i d x^2\right )\right )^{3/2}}+\frac {x}{\sqrt {a-i b \sin ^{-1}\left (1+i d x^2\right )}}}{3 b^2} \]

Antiderivative was successfully verified.

[In]

Integrate[(a - I*b*ArcSin[1 + I*d*x^2])^(-5/2),x]

[Out]

-1/3*((b*Sqrt[d*x^2*(-2*I + d*x^2)])/(d*x*(a - I*b*ArcSin[1 + I*d*x^2])^(3/2)) + x/Sqrt[a - I*b*ArcSin[1 + I*d
*x^2]] + (Sqrt[Pi]*x*FresnelC[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] - I*Si
nh[a/(2*b)]))/(Sqrt[(-I)*b]*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) + (Sqrt[Pi]*x*FresnelS[
Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Sqrt[(-I)*b]*(C
os[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])))/b^2

________________________________________________________________________________________

fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*arcsinh(-I+d*x^2))^(5/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

________________________________________________________________________________________

giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*arcsinh(-I+d*x^2))^(5/2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warn
ing, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was
done assuming [d,x]=[89,77]schur row 1 1.22263e-09Francis algorithm not precise enough for[1.0,0.0,-1.67068342
657e+12,-1.17545053497e+18,-2.32598592657e+23]Bad conditionned root j= 2 value -527644.406418 ratio 8.33415008
204 mindist 33.7256546889Warning, need to choose a branch for the root of a polynomial with parameters. This m
ight be wrong.The choice was done assuming [d,x]=[-66,8]schur row 1 9.91586e-07Francis algorithm not precise e
nough for[1.0,0.0,-107053064.0,602922946560,-9.55030161457e+14]Bad conditionned root j= 0 value 4231.08593187
ratio 1.71555050372 mindist 7.08837726861schur row 1 9.85057e-10Francis algorithm not precise enough for[1.0,0
.0,-137282971022,-2.76877787308e+16,-1.57055117809e+21]Unable to isolate roots number Vector [0,1][-0.15126799
6566355e6,-0.151267183209932e6]Bad conditionned root j= 2 value -151253.820244 ratio 2.23329136282 mindist 13.
3629663866Warning, choosing root of [1,0,%%%{-6,[2,4]%%%}+%%%{-8,[0,0]%%%},%%%{-8,[3,6]%%%}+%%%{-32,[1,2]%%%},
%%%{-3,[4,8]%%%}+%%%{-24,[2,4]%%%}+%%%{16,[0,0]%%%}] at parameters values [63,-49]Warning, need to choose a br
anch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d,x]=[84,
-65]Bad conditionned root j= 1 value -354917.321547 ratio 3.58199229828 mindist 17.6876820158Bad conditionned
root j= 2 value -354899.633865 ratio 36.3553454927 mindist 16.5892679524Bad conditionned root j= 1 value -3388
0.7669046 ratio 0.612379387673 mindist 0.825253607938Warning, choosing root of [1,0,%%%{-6,[2,4]%%%}+%%%{-8,[0
,0]%%%},%%%{-8,[3,6]%%%}+%%%{-32,[1,2]%%%},%%%{-3,[4,8]%%%}+%%%{-24,[2,4]%%%}+%%%{16,[0,0]%%%}] at parameters
values [70,22]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wro
ng.The choice was done assuming [d,x]=[30,-21]Warning, need to choose a branch for the root of a polynomial wi
th parameters. This might be wrong.The choice was done assuming [d,x]=[-24,-63]Warning, need to choose a branc
h for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d,x]=[11,52]
schur row 3 -3.22193e-07Warning, choosing root of [1,0,%%%{-4,[2,4]%%%}+%%%{-8,[0,0]%%%},%%%{-4,[3,6]%%%}+%%%{
-16,[1,2]%%%},%%%{-1,[4,8]%%%}+%%%{-4,[2,4]%%%}+%%%{16,[0,0]%%%}] at parameters values [18,-49]Warning, choosi
ng root of [1,0,%%%{-4,[2,4]%%%}+%%%{-8,[0,0]%%%},%%%{-4,[3,6]%%%}+%%%{-16,[1,2]%%%},%%%{-1,[4,8]%%%}+%%%{-4,[
2,4]%%%}+%%%{16,[0,0]%%%}] at parameters values [-33,-70]schur row 3 1.93169e-07Warning, choosing root of [1,0
,%%%{-4,[2,4]%%%}+%%%{-8,[0,0]%%%},%%%{-4,[3,6]%%%}+%%%{-16,[1,2]%%%},%%%{-1,[4,8]%%%}+%%%{-4,[2,4]%%%}+%%%{16
,[0,0]%%%}] at parameters values [8,63]Warning, need to choose a branch for the root of a polynomial with para
meters. This might be wrong.The choice was done assuming [d,x]=[-8,-94]schur row 1 1.15782e-08Francis algorith
m not precise enough for[1.0,0.0,-29980760072,2.82570662547e+15,-7.49038312879e+19]Bad conditionned root j= 0
value 70702.5530055 ratio 3.30491028239 mindist 18.5135468412Warning, need to choose a branch for the root of
a polynomial with parameters. This might be wrong.The choice was done assuming [d,x]=[-8,-38]schur row 1 3.472
75e-08Francis algorithm not precise enough for[1.0,0.0,-800692232.0,1.23327957985e+13,-5.34256730006e+16]Bad c
onditionned root j= 0 value 11555.1783957 ratio 1.30663425153 mindist 3.17957631341schur row 1 5.69583e-10Fran
cis algorithm not precise enough for[1.0,0.0,-1.32328584376e+12,-8.28597485843e+17,-1.45923785361e+23]Unable t
o isolate roots number Vector [0,2][-0.469612557480389e6,-0.469615331440520e6]Bad conditionned root j= 1 value
-469647.111085 ratio 3.72291056632 mindist 31.7796449475Warning, choosing root of [1,0,%%%{-6,[2,4]%%%}+%%%{-
8,[0,0]%%%},%%%{-8,[3,6]%%%}+%%%{-32,[1,2]%%%},%%%{-3,[4,8]%%%}+%%%{-24,[2,4]%%%}+%%%{16,[0,0]%%%}] at paramet
ers values [65,-85]Warning, need to choose a branch for the root of a polynomial with parameters. This might b
e wrong.The choice was done assuming [d,x]=[-86,73]Bad conditionned root j= 0 value 458272.621508 ratio 152.16
9961926 mindist 255.569113305Bad conditionned root j= 2 value 458592.326104 ratio 66.2919566381 mindist 302.96
7080007Bad conditionned root j= 1 value -770132.243981 ratio 141.661540265 mindist 52.7628472447Bad conditionn
ed root j= 2 value -770187.27489 ratio 12.2575973716 mindist 55.0309094898Unable to isolate roots number Vecto
r [1,3][-0.770132243980564e6,-0.770079481133319e6]Warning, choosing root of [1,0,%%%{-6,[2,4]%%%}+%%%{-8,[0,0]
%%%},%%%{-8,[3,6]%%%}+%%%{-32,[1,2]%%%},%%%{-3,[4,8]%%%}+%%%{-24,[2,4]%%%}+%%%{16,[0,0]%%%}] at parameters val
ues [93,91]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.
The choice was done assuming [d,x]=[-82,36]Warning, need to choose a branch for the root of a polynomial with
parameters. This might be wrong.The choice was done assuming [d,x]=[9,15]Warning, need to choose a branch for
the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d,x]=[-11,52]schur
row 3 1.00361e-07Warning, choosing root of [1,0,%%%{-4,[2,4]%%%}+%%%{-8,[0,0]%%%},%%%{-4,[3,6]%%%}+%%%{-16,[1
,2]%%%},%%%{-1,[4,8]%%%}+%%%{-4,[2,4]%%%}+%%%{16,[0,0]%%%}] at parameters values [79,-88]Warning, choosing roo
t of [1,0,%%%{-4,[2,4]%%%}+%%%{-8,[0,0]%%%},%%%{-4,[3,6]%%%}+%%%{-16,[1,2]%%%},%%%{-1,[4,8]%%%}+%%%{-4,[2,4]%%
%}+%%%{16,[0,0]%%%}] at parameters values [9,6]Warning, choosing root of [1,0,%%%{-4,[2,4]%%%}+%%%{-8,[0,0]%%%
},%%%{-4,[3,6]%%%}+%%%{-16,[1,2]%%%},%%%{-1,[4,8]%%%}+%%%{-4,[2,4]%%%}+%%%{16,[0,0]%%%}] at parameters values
[-69,-8]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The
choice was done assuming [d,t_nostep]=[91,52]Bad conditionned root j= 1 value -246064.602658 ratio 4.13844710
897 mindist 2.78272759262schur row 1 9.14435e-09Francis algorithm not precise enough for[1.0,0.0,-2124702752,-
5.33102089176e+13,-3.76196821029e+17]Bad conditionned root j= 1 value -18820.5074185 ratio 0.838796175516 mind
ist 3.20710914307Warning, choosing root of [1,0,%%%{-6,[2,4]%%%}+%%%{-8,[0,0]%%%},%%%{-8,[3,6]%%%}+%%%{-32,[1,
2]%%%},%%%{-3,[4,8]%%%}+%%%{-24,[2,4]%%%}+%%%{16,[0,0]%%%}] at parameters values [2,97]Warning, need to choose
a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d,t_
nostep]=[-82,75]schur row 1 1.2297e-10Francis algorithm not precise enough for[1.0,0.0,-1.27650937501e+12,7.85
05326564e+17,-1.35789682044e+23]Bad conditionned root j= 2 value 461240.783946 ratio 2.37092177178 mindist 11.
7745041251schur row 1 1.96129e-07Francis algorithm not precise enough for[1.0,0.0,-288648584.0,2.6694222528e+1
2,-6.94316785683e+15]Bad conditionned root j= 0 value 6940.98554667 ratio 1.29997372862 mindist 4.99589011288W
arning, choosing root of [1,0,%%%{-6,[2,4]%%%}+%%%{-8,[0,0]%%%},%%%{-8,[3,6]%%%}+%%%{-32,[1,2]%%%},%%%{-3,[4,8
]%%%}+%%%{-24,[2,4]%%%}+%%%{16,[0,0]%%%}] at parameters values [-24,-17]Evaluation time: 1.98sym2poly/r2sym(co
nst gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value

________________________________________________________________________________________

maple [F]  time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (a +b \arcsinh \left (d \,x^{2}-i\right )\right )^{\frac {5}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(a+b*arcsinh(-I+d*x^2))^(5/2),x)

[Out]

int(1/(a+b*arcsinh(-I+d*x^2))^(5/2),x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b \operatorname {arsinh}\left (d x^{2} - i\right ) + a\right )}^{\frac {5}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*arcsinh(-I+d*x^2))^(5/2),x, algorithm="maxima")

[Out]

integrate((b*arcsinh(d*x^2 - I) + a)^(-5/2), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {1}{{\left (a+b\,\mathrm {asinh}\left (d\,x^2-\mathrm {i}\right )\right )}^{5/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(a + b*asinh(d*x^2 - 1i))^(5/2),x)

[Out]

int(1/(a + b*asinh(d*x^2 - 1i))^(5/2), x)

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sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*asinh(-I+d*x**2))**(5/2),x)

[Out]

Exception raised: TypeError

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