3.9 Test file Number [206]

3.9.1 Fricas

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

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

[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