Question

integrate the function....

Answer 1

Using Product rule and appropriate substitution will lead us to answer.

Answer 2

Answer:

Step-by-step explanation:

xsin^- x

x∫sin^- x -∫∫sin^- x dx dx

∫sin^- x

xsin^- x +∫-x dx/√1-x^2

xsin^- x +1/2∫-2x dx /√1-x^2

xsin^- x +1/2∫dz/√z

xsin^- x +1/2(z)^1/2/1/2

xsin^- x +√z

xsin^- x +√1-x^2

therefore

x∫sin^- x - ∫∫sin^- x dx dx

x{xsin^- x +√1-x^2) - ∫xsin^- x +√1-x^2 dx

x{xsin^- x +√1-x^2}-∫xsin^- x -∫√1-x^2 dx

x{xsin^- x +√1-x^2} - ∫xsin^- dx -x√1-x^2/2 -(sin^- x) /2

∫xsin^- x =x{xsin^- x +√1-x^2} - ∫xsin^- dx -x√1-x^2/2 -sin^- x /2

2∫xsin^- x = x{xsin^- x +√1-x^2}-x√1-x^2/2 -(sin^- x) /2

∫xsin^- x =x{xsin^- x +√1-x^2}/2-x√1-x^2/4-(sin^- x )/4