following replacement u=cosx. (b) In the event your fuel out-of cosine was odd (n=2k+1), save one cosine factor and employ new https://datingranking.net/es/whatsyourprice-review/ label sin dos x + cos dos x = step one to alter the remaining products when it comes to sine.

next alternative u=sinx. (c) In case the vitality of one another sine and you will cosine is actually even then utilize the 50 % of direction identities.

By using the label sec 2 x = step one + tan 2 x we could move also efforts out of secant to help you tangent and the other way around

Since you will find learned approaches for solving integrals with factors from sine and you may cosine we can explore equivalent solutions to solve integrals which have circumstances away from tangent and secant.

Watching that (d/dx)tanx=sec dos x we could independent a factor regarding sec 2 x nonetheless remain which have a level fuel from secant. With the identity sec 2 x = step one + tan 2 x we could convert the remaining sec dos x so you’re able to an expression connected with tangent. Thus i’ve:

Note: Suppose we tried to use the substitution u=secx, then du=secxtanxdx. When we separate out a factor of secxtanx we are left with an odd power of tangent which is not easily converted to secant.

Note: Suppose we tried to use the substitution u=tanx, then du=sec 2 xdx. Read more