Question

integral (x^2+1) cos(x^3+3x+2) dx

Answer 1

∫(x²+1)cos(x³+3x+2) dx

let x³+3x+2= t

   differentiating both sides w.r.t  'x'

dt = (3x²+3) dx

dt = 3(x²+1) dx

divide both sides by 3,

dt/3= (x²+1)dx  ----------- (i)

put (i) back in the given expression,

I =1/3∫cost dt

I = 1/3sint +C         , where C is an arbitrary constant

put back value of  't'

I = 1/3 sin(x³+3x+2)