Question

sinx*sin3x
का समाकलन​

Answer 1

Answer:

integration of sinx/sin3x=

Step-by-step explanation:

sinxsin3x=sinxsinx(3cos2x−sin2x)  

=13cos2x−sin2x=12cos2x+cos2x

=12cos2x+1=sec2x3−tan2x( using cos2x=1−tan2x1+tan2x)

u=tanx,du=sec2xdx⇒∫13−u2du

u=3–√tanhw,du=3–√sech2wdw,w=tanh−1(tanx3–√)

∫13−u2du⇔13–√∫dw=w3–√+C

⇒∫sinxsin3xdx=tanh−1(tanx3√)3–√+C