3.9 Test file Number [206]

3.9.1 Fricas

Integral number [16] \[ \int \frac {\text {Si}(b x)^2}{x^3} \, dx \]

[B]   time = 0.369413 (sec), size = 87 ,normalized size = 6.69 \[ \frac {2 \, b^{2} x^{2} \operatorname {Ci}\left (2 \, b x\right ) + 2 \, b^{2} x^{2} \operatorname {Ci}\left (-2 \, b x\right ) - 2 \, b x \cos \left (b x\right ) \operatorname {Si}\left (b x\right ) - {\left (b^{2} x^{2} + 2\right )} \operatorname {Si}\left (b x\right )^{2} + \cos \left (b x\right )^{2} - 2 \, {\left (2 \, b x \cos \left (b x\right ) + \operatorname {Si}\left (b x\right )\right )} \sin \left (b x\right ) - 1}{4 \, x^{2}} \]

[In]

integrate(sin_integral(b*x)^2/x^3,x, algorithm=""fricas"")

[Out]

1/4*(2*b^2*x^2*cos_integral(2*b*x) + 2*b^2*x^2*cos_integral(-2*b*x) - 2*b*x*cos(b*x)*sin_integral(b*x) - (b^2*
x^2 + 2)*sin_integral(b*x)^2 + cos(b*x)^2 - 2*(2*b*x*cos(b*x) + sin_integral(b*x))*sin(b*x) - 1)/x^2