plz can u integrate sec^4 xdx thanks!
could someone please post a list of trig "recognition integrals" cos I never really spot them. Thank you x
There isn't really a definitive list, but there are a few identities and relationships you should always remember and try.
INT[cos^(n)x.sinx] = (-cos^(n+1)x)/(n+1)
INT[sin^(n)x.cosx] = (sin^(n+1)x)/(n+1)
INT[tan^(n)x.sec^2x] = (tan^(n+1)x)/(n+1)
INT[cot^(n)x.cosec^2x] = (-cot^(n+1)x)/(n+1)
sinx.cosx = ½sin2x, so INT[sinx.cosx] = -¼cos2x
These can be checked by differentiating.
Very useful identities:
1 + tan^2x = sec^2x
1 + cot^2x = cosec^2x
cos^2x = (cos2x + 1)/2