[itex]sec^{2}(x)tan(x)dx[/itex] Let U = sec(x) or tan(x) ?

[Lebombo]

The integral of $sec^{2}(x)tan(x)dx$ is what I'm asking about.

Homework Statement

$sec^{2}(x)tan(x)dx$

I can let u = tanx
then du = $sec^{2}(x)$

$\frac{1}{2}\int udu$

$\frac{1}{2}tan^{2}(x)$


OR

I can let u = secx
then du = secxtanx dx

$\int udu$

$\frac{1}{2}u^{2}$

$\frac{1}{2}sec^{2}(x)$


Why do both work? Which one is correct? Or are both correct?

 

[Dick]

The integral of $sec^{2}(x)tan(x)dx$ is what I'm asking about.

Homework Statement

$sec^{2}(x)tan(x)dx$

I can let u = tanx
then du = $sec^{2}(x)$

$\frac{1}{2}\int udu$

$\frac{1}{2}tan^{2}(x)$


OR

I can let u = secx
then du = secxtanx dx

$\int udu$

$\frac{1}{2}u^{2}$

$\frac{1}{2}sec^{2}(x)$


Why do both work? Which one is correct? Or are both correct?

They both work. They differ by a constant. sec(x)^2-tan(x)^2=1. You should put a '+C' in when you write the solution to an indefinite integral. That's where the difference is.

 

[Lebombo]

thanks, appreciate the feedback.