how do i integrate these? (1 Viewer)

[bos1234]

how do i integrate xcos2x

sec^4 x?

 

[Mattamz]

i dont think they would give you a question like this in 2u, without something like...

Find:
a) d/dx [(xsin2x)/2+(cos2x)/4}
b) Hence find Int(xcos2x)dx

if u do 4u maths could could do intergration by parts
ie.
let v = x u = (sin2x)/2
dv=dx du = cos2x.dx

Int(xcos2x)dx
= (xsin2x)/2 - Int((sin2x)/2)dx
=(xsin2x)/2 + (cos2x)/4 + C

 

[SoulSearcher]

For the second question, convert sec⁴x to sec²x * sec²x, then convert one of the sec²x terms into 1 + tan²x, expand the brackets and then integrate. You might need the substitution u = tan x for one of those terms.