intergral(tanx(secx)^2,x)

my book tells me to make u = sec(x) du = tanxsecx dxwhich makes sense, but could you also make u = tanx making du = (secx)^2 dx? But the latter method is incorrect why?

2. Originally Posted by s3n4te
intergral(tanx(secx)^2,x)

my book tells me to make u = sec(x) du = tanxsecx dxwhich makes sense,

but could you also make u = tanx making du = (secx)^2 dx? Mr F says: Yes. And, in my opinion, this is by far the simplest approach to take.

But the latter method is incorrect Mr F says: Says who!?

why? Mr F says: It's not incorrect. In fact, it's better!
..

3. Originally Posted by s3n4te
intergral(tanx(secx)^2,x)

my book tells me to make u = sec(x) du = tanxsecx dxwhich makes sense, but could you also make u = tanx making du = (secx)^2 dx? But the latter method is incorrect why?
Where did it say that the second way was incorrect? You could use either.

4. When I graphed both functions they aren't the same, is that normal?

5. Originally Posted by s3n4te
When I graphed both functions they aren't the same, is that normal?
The area under the curves will be the same which is what you are calculating using the integral.

6. oh that make sense :P

thanks