\(\int x^7 \operatorname {FresnelS}(b x)^2 \, dx\) [31]

Optimal result

Integrand size = 10, antiderivative size = 253 \[ \int x^7 \operatorname {FresnelS}(b x)^2 \, dx=-\frac {105 x^2}{16 b^6 \pi ^4}+\frac {7 x^6}{48 b^2 \pi ^2}-\frac {55 x^2 \cos \left (b^2 \pi x^2\right )}{16 b^6 \pi ^4}+\frac {x^6 \cos \left (b^2 \pi x^2\right )}{16 b^2 \pi ^2}-\frac {35 x^3 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b^5 \pi ^3}+\frac {x^7 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b \pi }-\frac {105 \operatorname {FresnelS}(b x)^2}{8 b^8 \pi ^4}+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2+\frac {105 x \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^7 \pi ^4}-\frac {7 x^5 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^3 \pi ^2}+\frac {10 \sin \left (b^2 \pi x^2\right )}{b^8 \pi ^5}-\frac {5 x^4 \sin \left (b^2 \pi x^2\right )}{8 b^4 \pi ^3} \]

[Out]

-105/16*x^2/b^6/Pi^4+7/48*x^6/b^2/Pi^2-55/16*x^2*cos(b^2*Pi*x^2)/b^6/Pi^4+1/16*x^6*cos(b^2*Pi*x^2)/b^2/Pi^2-35
/4*x^3*cos(1/2*b^2*Pi*x^2)*FresnelS(b*x)/b^5/Pi^3+1/4*x^7*cos(1/2*b^2*Pi*x^2)*FresnelS(b*x)/b/Pi-105/8*Fresnel
S(b*x)^2/b^8/Pi^4+1/8*x^8*FresnelS(b*x)^2+105/4*x*FresnelS(b*x)*sin(1/2*b^2*Pi*x^2)/b^7/Pi^4-7/4*x^5*FresnelS(
b*x)*sin(1/2*b^2*Pi*x^2)/b^3/Pi^2+10*sin(b^2*Pi*x^2)/b^8/Pi^5-5/8*x^4*sin(b^2*Pi*x^2)/b^4/Pi^3

Rubi [A] (verified)

Time = 0.31 (sec) , antiderivative size = 253, normalized size of antiderivative = 1.00, number of steps used = 23, number of rules used = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 1.000, Rules used = {6565, 6589, 6597, 3460, 3390, 30, 3377, 2717, 2714, 6575} \[ \int x^7 \operatorname {FresnelS}(b x)^2 \, dx=-\frac {105 \operatorname {FresnelS}(b x)^2}{8 \pi ^4 b^8}-\frac {105 x^2}{16 \pi ^4 b^6}+\frac {x^7 \operatorname {FresnelS}(b x) \cos \left (\frac {1}{2} \pi b^2 x^2\right )}{4 \pi b}+\frac {7 x^6}{48 \pi ^2 b^2}+\frac {x^6 \cos \left (\pi b^2 x^2\right )}{16 \pi ^2 b^2}+\frac {10 \sin \left (\pi b^2 x^2\right )}{\pi ^5 b^8}+\frac {105 x \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} \pi b^2 x^2\right )}{4 \pi ^4 b^7}-\frac {55 x^2 \cos \left (\pi b^2 x^2\right )}{16 \pi ^4 b^6}-\frac {35 x^3 \operatorname {FresnelS}(b x) \cos \left (\frac {1}{2} \pi b^2 x^2\right )}{4 \pi ^3 b^5}-\frac {5 x^4 \sin \left (\pi b^2 x^2\right )}{8 \pi ^3 b^4}-\frac {7 x^5 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} \pi b^2 x^2\right )}{4 \pi ^2 b^3}+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2 \]

[In]

Int[x^7*FresnelS[b*x]^2,x]

[Out]

(-105*x^2)/(16*b^6*Pi^4) + (7*x^6)/(48*b^2*Pi^2) - (55*x^2*Cos[b^2*Pi*x^2])/(16*b^6*Pi^4) + (x^6*Cos[b^2*Pi*x^
2])/(16*b^2*Pi^2) - (35*x^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(4*b^5*Pi^3) + (x^7*Cos[(b^2*Pi*x^2)/2]*Fresnel
S[b*x])/(4*b*Pi) - (105*FresnelS[b*x]^2)/(8*b^8*Pi^4) + (x^8*FresnelS[b*x]^2)/8 + (105*x*FresnelS[b*x]*Sin[(b^
2*Pi*x^2)/2])/(4*b^7*Pi^4) - (7*x^5*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(4*b^3*Pi^2) + (10*Sin[b^2*Pi*x^2])/(b^
8*Pi^5) - (5*x^4*Sin[b^2*Pi*x^2])/(8*b^4*Pi^3)

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rule 2714

Int[sin[(c_.) + ((d_.)*(x_))/2]^2, x_Symbol] :> Simp[x/2, x] - Simp[Sin[2*c + d*x]/(2*d), x] /; FreeQ[{c, d},
x]

Rule 2717

Int[sin[Pi/2 + (c_.) + (d_.)*(x_)], x_Symbol] :> Simp[Sin[c + d*x]/d, x] /; FreeQ[{c, d}, x]

Rule 3377

Int[((c_.) + (d_.)*(x_))^(m_.)*sin[(e_.) + (f_.)*(x_)], x_Symbol] :> Simp[(-(c + d*x)^m)*(Cos[e + f*x]/f), x]
+ Dist[d*(m/f), Int[(c + d*x)^(m - 1)*Cos[e + f*x], x], x] /; FreeQ[{c, d, e, f}, x] && GtQ[m, 0]

Rule 3390

Int[((c_.) + (d_.)*(x_))^(m_.)*sin[(e_.) + ((f_.)*(x_))/2]^2, x_Symbol] :> Dist[1/2, Int[(c + d*x)^m, x], x] -
Dist[1/2, Int[(c + d*x)^m*Cos[2*e + f*x], x], x] /; FreeQ[{c, d, e, f, m}, x]

Rule 3460

Int[(x_)^(m_.)*((a_.) + (b_.)*Sin[(c_.) + (d_.)*(x_)^(n_)])^(p_.), x_Symbol] :> Dist[1/n, Subst[Int[x^(Simplif
y[(m + 1)/n] - 1)*(a + b*Sin[c + d*x])^p, x], x, x^n], x] /; FreeQ[{a, b, c, d, m, n, p}, x] && IntegerQ[Simpl
ify[(m + 1)/n]] && (EqQ[p, 1] || EqQ[m, n - 1] || (IntegerQ[p] && GtQ[Simplify[(m + 1)/n], 0]))

Rule 6565

Int[FresnelS[(b_.)*(x_)]^2*(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)*(FresnelS[b*x]^2/(m + 1)), x] - Dist[2*(b/(
m + 1)), Int[x^(m + 1)*Sin[(Pi/2)*b^2*x^2]*FresnelS[b*x], x], x] /; FreeQ[b, x] && IntegerQ[m] && NeQ[m, -1]

Rule 6575

Int[FresnelS[(b_.)*(x_)]^(n_.)*Sin[(d_.)*(x_)^2], x_Symbol] :> Dist[Pi*(b/(2*d)), Subst[Int[x^n, x], x, Fresne
lS[b*x]], x] /; FreeQ[{b, d, n}, x] && EqQ[d^2, (Pi^2/4)*b^4]

Rule 6589

Int[FresnelS[(b_.)*(x_)]*(x_)^(m_)*Sin[(d_.)*(x_)^2], x_Symbol] :> Simp[(-x^(m - 1))*Cos[d*x^2]*(FresnelS[b*x]
/(2*d)), x] + (Dist[(m - 1)/(2*d), Int[x^(m - 2)*Cos[d*x^2]*FresnelS[b*x], x], x] + Dist[1/(2*b*Pi), Int[x^(m
- 1)*Sin[2*d*x^2], x], x]) /; FreeQ[{b, d}, x] && EqQ[d^2, (Pi^2/4)*b^4] && IGtQ[m, 1]

Rule 6597

Int[Cos[(d_.)*(x_)^2]*FresnelS[(b_.)*(x_)]*(x_)^(m_), x_Symbol] :> Simp[x^(m - 1)*Sin[d*x^2]*(FresnelS[b*x]/(2
*d)), x] + (-Dist[1/(Pi*b), Int[x^(m - 1)*Sin[d*x^2]^2, x], x] - Dist[(m - 1)/(2*d), Int[x^(m - 2)*Sin[d*x^2]*
FresnelS[b*x], x], x]) /; FreeQ[{b, d}, x] && EqQ[d^2, (Pi^2/4)*b^4] && IGtQ[m, 1]

Rubi steps \begin{align*} \text {integral}& = \frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2-\frac {1}{4} b \int x^8 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \\ & = \frac {x^7 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b \pi }+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2-\frac {\int x^7 \sin \left (b^2 \pi x^2\right ) \, dx}{8 \pi }-\frac {7 \int x^6 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x) \, dx}{4 b \pi } \\ & = \frac {x^7 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b \pi }+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2-\frac {7 x^5 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^3 \pi ^2}+\frac {35 \int x^4 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx}{4 b^3 \pi ^2}+\frac {7 \int x^5 \sin ^2\left (\frac {1}{2} b^2 \pi x^2\right ) \, dx}{4 b^2 \pi ^2}-\frac {\text {Subst}\left (\int x^3 \sin \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{16 \pi } \\ & = \frac {x^6 \cos \left (b^2 \pi x^2\right )}{16 b^2 \pi ^2}-\frac {35 x^3 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b^5 \pi ^3}+\frac {x^7 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b \pi }+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2-\frac {7 x^5 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^3 \pi ^2}+\frac {105 \int x^2 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x) \, dx}{4 b^5 \pi ^3}+\frac {35 \int x^3 \sin \left (b^2 \pi x^2\right ) \, dx}{8 b^4 \pi ^3}-\frac {3 \text {Subst}\left (\int x^2 \cos \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{16 b^2 \pi ^2}+\frac {7 \text {Subst}\left (\int x^2 \sin ^2\left (\frac {1}{2} b^2 \pi x\right ) \, dx,x,x^2\right )}{8 b^2 \pi ^2} \\ & = \frac {x^6 \cos \left (b^2 \pi x^2\right )}{16 b^2 \pi ^2}-\frac {35 x^3 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b^5 \pi ^3}+\frac {x^7 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b \pi }+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2+\frac {105 x \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^7 \pi ^4}-\frac {7 x^5 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^3 \pi ^2}-\frac {3 x^4 \sin \left (b^2 \pi x^2\right )}{16 b^4 \pi ^3}-\frac {105 \int \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx}{4 b^7 \pi ^4}-\frac {105 \int x \sin ^2\left (\frac {1}{2} b^2 \pi x^2\right ) \, dx}{4 b^6 \pi ^4}+\frac {3 \text {Subst}\left (\int x \sin \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{8 b^4 \pi ^3}+\frac {35 \text {Subst}\left (\int x \sin \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{16 b^4 \pi ^3}+\frac {7 \text {Subst}\left (\int x^2 \, dx,x,x^2\right )}{16 b^2 \pi ^2}-\frac {7 \text {Subst}\left (\int x^2 \cos \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{16 b^2 \pi ^2} \\ & = \frac {7 x^6}{48 b^2 \pi ^2}-\frac {41 x^2 \cos \left (b^2 \pi x^2\right )}{16 b^6 \pi ^4}+\frac {x^6 \cos \left (b^2 \pi x^2\right )}{16 b^2 \pi ^2}-\frac {35 x^3 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b^5 \pi ^3}+\frac {x^7 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b \pi }+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2+\frac {105 x \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^7 \pi ^4}-\frac {7 x^5 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^3 \pi ^2}-\frac {5 x^4 \sin \left (b^2 \pi x^2\right )}{8 b^4 \pi ^3}-\frac {105 \text {Subst}(\int x \, dx,x,\operatorname {FresnelS}(b x))}{4 b^8 \pi ^4}+\frac {3 \text {Subst}\left (\int \cos \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{8 b^6 \pi ^4}+\frac {35 \text {Subst}\left (\int \cos \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{16 b^6 \pi ^4}-\frac {105 \text {Subst}\left (\int \sin ^2\left (\frac {1}{2} b^2 \pi x\right ) \, dx,x,x^2\right )}{8 b^6 \pi ^4}+\frac {7 \text {Subst}\left (\int x \sin \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{8 b^4 \pi ^3} \\ & = -\frac {105 x^2}{16 b^6 \pi ^4}+\frac {7 x^6}{48 b^2 \pi ^2}-\frac {55 x^2 \cos \left (b^2 \pi x^2\right )}{16 b^6 \pi ^4}+\frac {x^6 \cos \left (b^2 \pi x^2\right )}{16 b^2 \pi ^2}-\frac {35 x^3 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b^5 \pi ^3}+\frac {x^7 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b \pi }-\frac {105 \operatorname {FresnelS}(b x)^2}{8 b^8 \pi ^4}+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2+\frac {105 x \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^7 \pi ^4}-\frac {7 x^5 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^3 \pi ^2}+\frac {73 \sin \left (b^2 \pi x^2\right )}{8 b^8 \pi ^5}-\frac {5 x^4 \sin \left (b^2 \pi x^2\right )}{8 b^4 \pi ^3}+\frac {7 \text {Subst}\left (\int \cos \left (b^2 \pi x\right ) \, dx,x,x^2\right )}{8 b^6 \pi ^4} \\ & = -\frac {105 x^2}{16 b^6 \pi ^4}+\frac {7 x^6}{48 b^2 \pi ^2}-\frac {55 x^2 \cos \left (b^2 \pi x^2\right )}{16 b^6 \pi ^4}+\frac {x^6 \cos \left (b^2 \pi x^2\right )}{16 b^2 \pi ^2}-\frac {35 x^3 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b^5 \pi ^3}+\frac {x^7 \cos \left (\frac {1}{2} b^2 \pi x^2\right ) \operatorname {FresnelS}(b x)}{4 b \pi }-\frac {105 \operatorname {FresnelS}(b x)^2}{8 b^8 \pi ^4}+\frac {1}{8} x^8 \operatorname {FresnelS}(b x)^2+\frac {105 x \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^7 \pi ^4}-\frac {7 x^5 \operatorname {FresnelS}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{4 b^3 \pi ^2}+\frac {10 \sin \left (b^2 \pi x^2\right )}{b^8 \pi ^5}-\frac {5 x^4 \sin \left (b^2 \pi x^2\right )}{8 b^4 \pi ^3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 181, normalized size of antiderivative = 0.72 \[ \int x^7 \operatorname {FresnelS}(b x)^2 \, dx=\frac {-315 b^2 \pi x^2+7 b^6 \pi ^3 x^6+3 b^2 \pi x^2 \left (-55+b^4 \pi ^2 x^4\right ) \cos \left (b^2 \pi x^2\right )+6 \pi \left (-105+b^8 \pi ^4 x^8\right ) \operatorname {FresnelS}(b x)^2+12 b \pi x \operatorname {FresnelS}(b x) \left (b^2 \pi x^2 \left (-35+b^4 \pi ^2 x^4\right ) \cos \left (\frac {1}{2} b^2 \pi x^2\right )-7 \left (-15+b^4 \pi ^2 x^4\right ) \sin \left (\frac {1}{2} b^2 \pi x^2\right )\right )+480 \sin \left (b^2 \pi x^2\right )-30 b^4 \pi ^2 x^4 \sin \left (b^2 \pi x^2\right )}{48 b^8 \pi ^5} \]

[In]

Integrate[x^7*FresnelS[b*x]^2,x]

[Out]

(-315*b^2*Pi*x^2 + 7*b^6*Pi^3*x^6 + 3*b^2*Pi*x^2*(-55 + b^4*Pi^2*x^4)*Cos[b^2*Pi*x^2] + 6*Pi*(-105 + b^8*Pi^4*
x^8)*FresnelS[b*x]^2 + 12*b*Pi*x*FresnelS[b*x]*(b^2*Pi*x^2*(-35 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] - 7*(-15 +
b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) + 480*Sin[b^2*Pi*x^2] - 30*b^4*Pi^2*x^4*Sin[b^2*Pi*x^2])/(48*b^8*Pi^5)

Maple [F]

\[\int x^{7} \operatorname {FresnelS}\left (b x \right )^{2}d x\]

[In]

int(x^7*FresnelS(b*x)^2,x)

[Out]

int(x^7*FresnelS(b*x)^2,x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 183, normalized size of antiderivative = 0.72 \[ \int x^7 \operatorname {FresnelS}(b x)^2 \, dx=\frac {2 \, \pi ^{3} b^{6} x^{6} - 75 \, \pi b^{2} x^{2} + 3 \, {\left (\pi ^{3} b^{6} x^{6} - 55 \, \pi b^{2} x^{2}\right )} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )^{2} + 6 \, {\left (\pi ^{4} b^{7} x^{7} - 35 \, \pi ^{2} b^{3} x^{3}\right )} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) \operatorname {S}\left (b x\right ) - 3 \, {\left (105 \, \pi - \pi ^{5} b^{8} x^{8}\right )} \operatorname {S}\left (b x\right )^{2} - 6 \, {\left (5 \, {\left (\pi ^{2} b^{4} x^{4} - 16\right )} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + 7 \, {\left (\pi ^{3} b^{5} x^{5} - 15 \, \pi b x\right )} \operatorname {S}\left (b x\right )\right )} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{24 \, \pi ^{5} b^{8}} \]

[In]

integrate(x^7*fresnel_sin(b*x)^2,x, algorithm="fricas")

[Out]

1/24*(2*pi^3*b^6*x^6 - 75*pi*b^2*x^2 + 3*(pi^3*b^6*x^6 - 55*pi*b^2*x^2)*cos(1/2*pi*b^2*x^2)^2 + 6*(pi^4*b^7*x^
7 - 35*pi^2*b^3*x^3)*cos(1/2*pi*b^2*x^2)*fresnel_sin(b*x) - 3*(105*pi - pi^5*b^8*x^8)*fresnel_sin(b*x)^2 - 6*(
5*(pi^2*b^4*x^4 - 16)*cos(1/2*pi*b^2*x^2) + 7*(pi^3*b^5*x^5 - 15*pi*b*x)*fresnel_sin(b*x))*sin(1/2*pi*b^2*x^2)
)/(pi^5*b^8)

Sympy [F]

\[ \int x^7 \operatorname {FresnelS}(b x)^2 \, dx=\int x^{7} S^{2}\left (b x\right )\, dx \]

[In]

integrate(x**7*fresnels(b*x)**2,x)

[Out]

Integral(x**7*fresnels(b*x)**2, x)

Maxima [F]

\[ \int x^7 \operatorname {FresnelS}(b x)^2 \, dx=\int { x^{7} \operatorname {S}\left (b x\right )^{2} \,d x } \]

[In]

integrate(x^7*fresnel_sin(b*x)^2,x, algorithm="maxima")

[Out]

integrate(x^7*fresnel_sin(b*x)^2, x)

Giac [F]

\[ \int x^7 \operatorname {FresnelS}(b x)^2 \, dx=\int { x^{7} \operatorname {S}\left (b x\right )^{2} \,d x } \]

[In]

integrate(x^7*fresnel_sin(b*x)^2,x, algorithm="giac")

[Out]

integrate(x^7*fresnel_sin(b*x)^2, x)

Mupad [F(-1)]

Timed out. \[ \int x^7 \operatorname {FresnelS}(b x)^2 \, dx=\int x^7\,{\mathrm {FresnelS}\left (b\,x\right )}^2 \,d x \]

[In]

int(x^7*FresnelS(b*x)^2,x)

[Out]

int(x^7*FresnelS(b*x)^2, x)