3.58 \(\int \frac{\text{csch}^3(c+d x)}{(a+b \sinh ^2(c+d x))^3} \, dx\)

Optimal. Leaf size=224 \[ \frac{b^{3/2} \left (35 a^2-56 a b+24 b^2\right ) \tan ^{-1}\left (\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right )}{8 a^4 d (a-b)^{5/2}}-\frac{b (a-4 b) (4 a-3 b) \cosh (c+d x)}{8 a^3 d (a-b)^2 \left (a+b \cosh ^2(c+d x)-b\right )}-\frac{b (2 a-3 b) \cosh (c+d x)}{4 a^2 d (a-b) \left (a+b \cosh ^2(c+d x)-b\right )^2}+\frac{(a+6 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^4 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left (a+b \cosh ^2(c+d x)-b\right )^2} \]

[Out]

(b^(3/2)*(35*a^2 - 56*a*b + 24*b^2)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(8*a^4*(a - b)^(5/2)*d) + ((a
+ 6*b)*ArcTanh[Cosh[c + d*x]])/(2*a^4*d) - ((2*a - 3*b)*b*Cosh[c + d*x])/(4*a^2*(a - b)*d*(a - b + b*Cosh[c +
d*x]^2)^2) - ((a - 4*b)*(4*a - 3*b)*b*Cosh[c + d*x])/(8*a^3*(a - b)^2*d*(a - b + b*Cosh[c + d*x]^2)) - (Coth[
c + d*x]*Csch[c + d*x])/(2*a*d*(a - b + b*Cosh[c + d*x]^2)^2)

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Rubi [A]  time = 0.43874, antiderivative size = 224, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 6, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.261, Rules used = {3186, 414, 527, 522, 206, 205} \[ \frac{b^{3/2} \left (35 a^2-56 a b+24 b^2\right ) \tan ^{-1}\left (\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right )}{8 a^4 d (a-b)^{5/2}}-\frac{b (a-4 b) (4 a-3 b) \cosh (c+d x)}{8 a^3 d (a-b)^2 \left (a+b \cosh ^2(c+d x)-b\right )}-\frac{b (2 a-3 b) \cosh (c+d x)}{4 a^2 d (a-b) \left (a+b \cosh ^2(c+d x)-b\right )^2}+\frac{(a+6 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^4 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left (a+b \cosh ^2(c+d x)-b\right )^2} \]

Antiderivative was successfully verified.

[In]

Int[Csch[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^3,x]

[Out]

(b^(3/2)*(35*a^2 - 56*a*b + 24*b^2)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(8*a^4*(a - b)^(5/2)*d) + ((a
+ 6*b)*ArcTanh[Cosh[c + d*x]])/(2*a^4*d) - ((2*a - 3*b)*b*Cosh[c + d*x])/(4*a^2*(a - b)*d*(a - b + b*Cosh[c +
d*x]^2)^2) - ((a - 4*b)*(4*a - 3*b)*b*Cosh[c + d*x])/(8*a^3*(a - b)^2*d*(a - b + b*Cosh[c + d*x]^2)) - (Coth[
c + d*x]*Csch[c + d*x])/(2*a*d*(a - b + b*Cosh[c + d*x]^2)^2)

Rule 3186

Int[sin[(e_.) + (f_.)*(x_)]^(m_.)*((a_) + (b_.)*sin[(e_.) + (f_.)*(x_)]^2)^(p_.), x_Symbol] :> With[{ff = Free
Factors[Cos[e + f*x], x]}, -Dist[ff/f, Subst[Int[(1 - ff^2*x^2)^((m - 1)/2)*(a + b - b*ff^2*x^2)^p, x], x, Cos
[e + f*x]/ff], x]] /; FreeQ[{a, b, e, f, p}, x] && IntegerQ[(m - 1)/2]

Rule 414

Int[((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> -Simp[(b*x*(a + b*x^n)^(p + 1)*(
c + d*x^n)^(q + 1))/(a*n*(p + 1)*(b*c - a*d)), x] + Dist[1/(a*n*(p + 1)*(b*c - a*d)), Int[(a + b*x^n)^(p + 1)*
(c + d*x^n)^q*Simp[b*c + n*(p + 1)*(b*c - a*d) + d*b*(n*(p + q + 2) + 1)*x^n, x], x], x] /; FreeQ[{a, b, c, d,
n, q}, x] && NeQ[b*c - a*d, 0] && LtQ[p, -1] &&  !( !IntegerQ[p] && IntegerQ[q] && LtQ[q, -1]) && IntBinomial
Q[a, b, c, d, n, p, q, x]

Rule 527

Int[((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_.)*((e_) + (f_.)*(x_)^(n_)), x_Symbol] :> -Simp[
((b*e - a*f)*x*(a + b*x^n)^(p + 1)*(c + d*x^n)^(q + 1))/(a*n*(b*c - a*d)*(p + 1)), x] + Dist[1/(a*n*(b*c - a*d
)*(p + 1)), Int[(a + b*x^n)^(p + 1)*(c + d*x^n)^q*Simp[c*(b*e - a*f) + e*n*(b*c - a*d)*(p + 1) + d*(b*e - a*f)
*(n*(p + q + 2) + 1)*x^n, x], x], x] /; FreeQ[{a, b, c, d, e, f, n, q}, x] && LtQ[p, -1]

Rule 522

Int[((e_) + (f_.)*(x_)^(n_))/(((a_) + (b_.)*(x_)^(n_))*((c_) + (d_.)*(x_)^(n_))), x_Symbol] :> Dist[(b*e - a*f
)/(b*c - a*d), Int[1/(a + b*x^n), x], x] - Dist[(d*e - c*f)/(b*c - a*d), Int[1/(c + d*x^n), x], x] /; FreeQ[{a
, b, c, d, e, f, n}, x]

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 205

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

Rubi steps

\begin{align*} \int \frac{\text{csch}^3(c+d x)}{\left (a+b \sinh ^2(c+d x)\right )^3} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{1}{\left (1-x^2\right )^2 \left (a-b+b x^2\right )^3} \, dx,x,\cosh (c+d x)\right )}{d}\\ &=-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left (a-b+b \cosh ^2(c+d x)\right )^2}+\frac{\operatorname{Subst}\left (\int \frac{a+b+5 b x^2}{\left (1-x^2\right ) \left (a-b+b x^2\right )^3} \, dx,x,\cosh (c+d x)\right )}{2 a d}\\ &=-\frac{(2 a-3 b) b \cosh (c+d x)}{4 a^2 (a-b) d \left (a-b+b \cosh ^2(c+d x)\right )^2}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left (a-b+b \cosh ^2(c+d x)\right )^2}-\frac{\operatorname{Subst}\left (\int \frac{-2 \left (2 a^2+4 a b-3 b^2\right )-6 (2 a-3 b) b x^2}{\left (1-x^2\right ) \left (a-b+b x^2\right )^2} \, dx,x,\cosh (c+d x)\right )}{8 a^2 (a-b) d}\\ &=-\frac{(2 a-3 b) b \cosh (c+d x)}{4 a^2 (a-b) d \left (a-b+b \cosh ^2(c+d x)\right )^2}-\frac{(a-4 b) (4 a-3 b) b \cosh (c+d x)}{8 a^3 (a-b)^2 d \left (a-b+b \cosh ^2(c+d x)\right )}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left (a-b+b \cosh ^2(c+d x)\right )^2}+\frac{\operatorname{Subst}\left (\int \frac{2 \left (4 a^3+12 a^2 b-25 a b^2+12 b^3\right )+2 (a-4 b) (4 a-3 b) b x^2}{\left (1-x^2\right ) \left (a-b+b x^2\right )} \, dx,x,\cosh (c+d x)\right )}{16 a^3 (a-b)^2 d}\\ &=-\frac{(2 a-3 b) b \cosh (c+d x)}{4 a^2 (a-b) d \left (a-b+b \cosh ^2(c+d x)\right )^2}-\frac{(a-4 b) (4 a-3 b) b \cosh (c+d x)}{8 a^3 (a-b)^2 d \left (a-b+b \cosh ^2(c+d x)\right )}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left (a-b+b \cosh ^2(c+d x)\right )^2}+\frac{(a+6 b) \operatorname{Subst}\left (\int \frac{1}{1-x^2} \, dx,x,\cosh (c+d x)\right )}{2 a^4 d}+\frac{\left (b^2 \left (35 a^2-56 a b+24 b^2\right )\right ) \operatorname{Subst}\left (\int \frac{1}{a-b+b x^2} \, dx,x,\cosh (c+d x)\right )}{8 a^4 (a-b)^2 d}\\ &=\frac{b^{3/2} \left (35 a^2-56 a b+24 b^2\right ) \tan ^{-1}\left (\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right )}{8 a^4 (a-b)^{5/2} d}+\frac{(a+6 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^4 d}-\frac{(2 a-3 b) b \cosh (c+d x)}{4 a^2 (a-b) d \left (a-b+b \cosh ^2(c+d x)\right )^2}-\frac{(a-4 b) (4 a-3 b) b \cosh (c+d x)}{8 a^3 (a-b)^2 d \left (a-b+b \cosh ^2(c+d x)\right )}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left (a-b+b \cosh ^2(c+d x)\right )^2}\\ \end{align*}

Mathematica [C]  time = 2.94302, size = 419, normalized size = 1.87 \[ \frac{\text{csch}^5(c+d x) (2 a+b \cosh (2 (c+d x))-b) \left (\frac{8 a^2 b^2 \coth (c+d x)}{a-b}+\frac{b^{3/2} \left (35 a^2-56 a b+24 b^2\right ) \text{csch}(c+d x) (2 a+b \cosh (2 (c+d x))-b)^2 \tan ^{-1}\left (\frac{\sqrt{b}-i \sqrt{a} \tanh \left (\frac{1}{2} (c+d x)\right )}{\sqrt{a-b}}\right )}{(a-b)^{5/2}}+\frac{b^{3/2} \left (35 a^2-56 a b+24 b^2\right ) \text{csch}(c+d x) (2 a+b \cosh (2 (c+d x))-b)^2 \tan ^{-1}\left (\frac{\sqrt{b}+i \sqrt{a} \tanh \left (\frac{1}{2} (c+d x)\right )}{\sqrt{a-b}}\right )}{(a-b)^{5/2}}+\frac{2 a b^2 (11 a-8 b) \coth (c+d x) (2 a+b \cosh (2 (c+d x))-b)}{(a-b)^2}-a \text{csch}^2\left (\frac{1}{2} (c+d x)\right ) \text{csch}(c+d x) (2 a+b \cosh (2 (c+d x))-b)^2-a \text{csch}(c+d x) \text{sech}^2\left (\frac{1}{2} (c+d x)\right ) (2 a+b \cosh (2 (c+d x))-b)^2-4 (a+6 b) \text{csch}(c+d x) \log \left (\tanh \left (\frac{1}{2} (c+d x)\right )\right ) (2 a+b \cosh (2 (c+d x))-b)^2\right )}{64 a^4 d \left (a \text{csch}^2(c+d x)+b\right )^3} \]

Antiderivative was successfully verified.

[In]

Integrate[Csch[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^3,x]

[Out]

((2*a - b + b*Cosh[2*(c + d*x)])*Csch[c + d*x]^5*((8*a^2*b^2*Coth[c + d*x])/(a - b) + (2*a*(11*a - 8*b)*b^2*(2
*a - b + b*Cosh[2*(c + d*x)])*Coth[c + d*x])/(a - b)^2 + (b^(3/2)*(35*a^2 - 56*a*b + 24*b^2)*ArcTan[(Sqrt[b] -
I*Sqrt[a]*Tanh[(c + d*x)/2])/Sqrt[a - b]]*(2*a - b + b*Cosh[2*(c + d*x)])^2*Csch[c + d*x])/(a - b)^(5/2) + (b
^(3/2)*(35*a^2 - 56*a*b + 24*b^2)*ArcTan[(Sqrt[b] + I*Sqrt[a]*Tanh[(c + d*x)/2])/Sqrt[a - b]]*(2*a - b + b*Cos
h[2*(c + d*x)])^2*Csch[c + d*x])/(a - b)^(5/2) - a*(2*a - b + b*Cosh[2*(c + d*x)])^2*Csch[(c + d*x)/2]^2*Csch[
c + d*x] - 4*(a + 6*b)*(2*a - b + b*Cosh[2*(c + d*x)])^2*Csch[c + d*x]*Log[Tanh[(c + d*x)/2]] - a*(2*a - b + b
*Cosh[2*(c + d*x)])^2*Csch[c + d*x]*Sech[(c + d*x)/2]^2))/(64*a^4*d*(b + a*Csch[c + d*x]^2)^3)

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Maple [B]  time = 0.091, size = 1225, normalized size = 5.5 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(csch(d*x+c)^3/(a+b*sinh(d*x+c)^2)^3,x)

[Out]

1/8/d*tanh(1/2*d*x+1/2*c)^2/a^3-1/8/d/a^3/tanh(1/2*d*x+1/2*c)^2-1/2/d/a^3*ln(tanh(1/2*d*x+1/2*c))-3/d/a^4*ln(t
anh(1/2*d*x+1/2*c))*b-13/4/d/(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2
/a/(a^2-2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^6*b^2+10/d/a^2*b^3/(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4
*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2-2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^6-6/d*b^4/a^3/(tanh(1/2*d*x+1/2*c)^4*a-2*tan
h(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2-2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^6+39/4/d/(tanh(1/2*d*x
+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*b^2/(a^2-2*a*b+b^2)*tanh(1/2*d*x+1/2*c)
^4-67/2/d/(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2/(a^2-2*a*b+b^2
)*tanh(1/2*d*x+1/2*c)^4*b^3+46/d/a^3*b^4/(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2
*c)^2*b+a)^2/(a^2-2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^4-20/d*b^5/a^4/(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)
^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2-2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^4-39/4/d/(tanh(1/2*d*x+1/2*c)^4*a-2*ta
nh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a/(a^2-2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^2*b^2+26/d/a^2*b^3/
(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2-2*a*b+b^2)*tanh(1/2*d*x
+1/2*c)^2-14/d*b^4/a^3/(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2-
2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^2+13/4/d/a*b^2/(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*
x+1/2*c)^2*b+a)^2/(a^2-2*a*b+b^2)-5/2/d*b^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a-2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*
d*x+1/2*c)^2*b+a)^2/(a^2-2*a*b+b^2)+35/8/d/a^2*b^2/(a^2-2*a*b+b^2)/(a*b-b^2)^(1/2)*arctan(1/4*(2*tanh(1/2*d*x+
1/2*c)^2*a-2*a+4*b)/(a*b-b^2)^(1/2))-7/d/a^3*b^3/(a^2-2*a*b+b^2)/(a*b-b^2)^(1/2)*arctan(1/4*(2*tanh(1/2*d*x+1/
2*c)^2*a-2*a+4*b)/(a*b-b^2)^(1/2))+3/d*b^4/a^4/(a^2-2*a*b+b^2)/(a*b-b^2)^(1/2)*arctan(1/4*(2*tanh(1/2*d*x+1/2*
c)^2*a-2*a+4*b)/(a*b-b^2)^(1/2))

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Maxima [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(d*x+c)^3/(a+b*sinh(d*x+c)^2)^3,x, algorithm="maxima")

[Out]

-1/4*((4*a^2*b^2*e^(11*c) - 19*a*b^3*e^(11*c) + 12*b^4*e^(11*c))*e^(11*d*x) + (32*a^3*b*e^(9*c) - 128*a^2*b^2*
e^(9*c) + 129*a*b^3*e^(9*c) - 36*b^4*e^(9*c))*e^(9*d*x) + 2*(32*a^4*e^(7*c) - 80*a^3*b*e^(7*c) + 94*a^2*b^2*e^
(7*c) - 55*a*b^3*e^(7*c) + 12*b^4*e^(7*c))*e^(7*d*x) + 2*(32*a^4*e^(5*c) - 80*a^3*b*e^(5*c) + 94*a^2*b^2*e^(5*
c) - 55*a*b^3*e^(5*c) + 12*b^4*e^(5*c))*e^(5*d*x) + (32*a^3*b*e^(3*c) - 128*a^2*b^2*e^(3*c) + 129*a*b^3*e^(3*c
) - 36*b^4*e^(3*c))*e^(3*d*x) + (4*a^2*b^2*e^c - 19*a*b^3*e^c + 12*b^4*e^c)*e^(d*x))/(a^5*b^2*d - 2*a^4*b^3*d
+ a^3*b^4*d + (a^5*b^2*d*e^(12*c) - 2*a^4*b^3*d*e^(12*c) + a^3*b^4*d*e^(12*c))*e^(12*d*x) + 2*(4*a^6*b*d*e^(10
*c) - 11*a^5*b^2*d*e^(10*c) + 10*a^4*b^3*d*e^(10*c) - 3*a^3*b^4*d*e^(10*c))*e^(10*d*x) + (16*a^7*d*e^(8*c) - 6
4*a^6*b*d*e^(8*c) + 95*a^5*b^2*d*e^(8*c) - 62*a^4*b^3*d*e^(8*c) + 15*a^3*b^4*d*e^(8*c))*e^(8*d*x) - 4*(8*a^7*d
*e^(6*c) - 28*a^6*b*d*e^(6*c) + 37*a^5*b^2*d*e^(6*c) - 22*a^4*b^3*d*e^(6*c) + 5*a^3*b^4*d*e^(6*c))*e^(6*d*x) +
(16*a^7*d*e^(4*c) - 64*a^6*b*d*e^(4*c) + 95*a^5*b^2*d*e^(4*c) - 62*a^4*b^3*d*e^(4*c) + 15*a^3*b^4*d*e^(4*c))*
e^(4*d*x) + 2*(4*a^6*b*d*e^(2*c) - 11*a^5*b^2*d*e^(2*c) + 10*a^4*b^3*d*e^(2*c) - 3*a^3*b^4*d*e^(2*c))*e^(2*d*x
)) + 1/2*(a + 6*b)*log((e^(d*x + c) + 1)*e^(-c))/(a^4*d) - 1/2*(a + 6*b)*log((e^(d*x + c) - 1)*e^(-c))/(a^4*d)
+ 8*integrate(1/32*((35*a^2*b^2*e^(3*c) - 56*a*b^3*e^(3*c) + 24*b^4*e^(3*c))*e^(3*d*x) - (35*a^2*b^2*e^c - 56
*a*b^3*e^c + 24*b^4*e^c)*e^(d*x))/(a^6*b - 2*a^5*b^2 + a^4*b^3 + (a^6*b*e^(4*c) - 2*a^5*b^2*e^(4*c) + a^4*b^3*
e^(4*c))*e^(4*d*x) + 2*(2*a^7*e^(2*c) - 5*a^6*b*e^(2*c) + 4*a^5*b^2*e^(2*c) - a^4*b^3*e^(2*c))*e^(2*d*x)), x)

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Fricas [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(d*x+c)^3/(a+b*sinh(d*x+c)^2)^3,x, algorithm="fricas")

[Out]

Timed out

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(d*x+c)**3/(a+b*sinh(d*x+c)**2)**3,x)

[Out]

Timed out

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Giac [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(d*x+c)^3/(a+b*sinh(d*x+c)^2)^3,x, algorithm="giac")

[Out]

Exception raised: TypeError