Hello Aspirant,

Hope you are doing well!!

It is quite difficult to make integration sign, In place of integration sign I'll put |, and in place of power I'll put **  when you are solve in your notebook you can place | sign to integration sign and ** to power sign.

Let X+Y = v

1 + dY/dX = dv/dX

dY/dX= dv/dX-1

dY/dX = sin (X + Y) + cos (X + Y)

dv/dX - 1 = sin v + cos v

dv / (1+cos v + sin v) = dX

Integrate both side

| dv / (1 + cos v + sin v ) = | dX | dv / ( 1 + ((1 - tan**2 (v/2)) / (1 + tan** 2 (v/2)) + ((2 tan (v/2) / (1 + tan **2 (v/2))

= |dX | sec**2 (v/2) dv / (2(1+ tan(v/2))

=|dx log (1 + tan (v/2)

= X+ c log ( 1+ tan (X + Y) / 2) = X + c

I hope this will help you.

Feel free to ask any query.

Hi Aspirant,

Yes you can easily do the sum by the process of differential differentiation and integration.Move the dx to the right side  and then making appropriate arrangements integrate the whole left side and the right side and the question will easily get solved.

Hope it helps!!!