Question

everybody can solve it​

Answer 1

Ok but what
There is no Question if you know everybody can solve it then why are you asking.

Answer 2

taken sign of itegration is f

let x = sin^6t

so in inverse form

t = sin^-1x^1/5

diffrenciating with respect to t

dx = 6sin^5tcostdt

f6{sin^5tcost/(sin^3t + sin^2t )}dt

6fsin^3tcost/(sint+1)dt

6fsin^2tcost/(1+1/sint)dt

let

1+1/sint = z

diffrenciating with Respect to z we get

- (cost/sin^2t)dt= dz

-sin^2tdt = dz/cost

- 6f(1/z)dz

-12sqrt z +c

-12sqrt(1+1/sint)+c

-12 sqrt( 1+ 1/sinsin^-1x^1/6)+c

-12sqrt(1+1/x^6) + c

may be help you