dsin-13x-4x3dx=
31-x2
-11-x2
1
none of these
Explanation for correct option:
Step-1: Simplify the given data.
Given, dsin-13x-4x3dx
Put, x=sinθ⇒θ=sin-1x
⇒dsin-13x-4x3dx=dsin-13sinθ-4sinθ3dx
Apply formula,
3sinθ-4sin3θ=sin3θ
=dsin-1sin3θdx=d3sin-1xdx
Step-2: Differentiate w.r.t x
⇒d3sin-1xdx=3×11-x2∵sin-1x=11-x2⇒d3sin-1xdx=31-x2
Therefore, correct answer is option A