TyErd's questions

[TyErd]

anti-derivative of tan(kx)?

[TyErd]

just a tip, taking out the constant has no effect and will make things simpler.

What do you mean? can you give an example please

[brightsky]

just a tip, taking out the constant has no effect and will make things simpler.

What do you mean? can you give an example please

Just as in your previous example, , we can simplify this down to .

[TyErd]

OH yeas Thanks!

[superflya]

anti-derivative of tan(kx)?

ln|sec(x)|

[the.watchman]

anti-derivative of tan(kx)?

There is no 'methods' anti-derivative of tan, so don't worry about it (unless you do spesh, in which case, you should know it)

just a tip, taking out the constant has no effect and will make things simpler.

What do you mean? can you give an example please

Just as in your previous example, , we can simplify this down to .

This brings up another important point:

If a question is: Find the antiderivative of

There are many answers, one of which is , another is , depending on what method you choose

Now most of you will already know this, but because
They are all equivalent, as is a constant
So if the textbook has/lacks a constant inside the log, it doesn't matter

EDIT: Sorry to overlap your post superflya, but I'm a very slow typer...

[brightsky]

anti-derivative of tan(kx)?

First find :

We know that

Make substitution , then

So the original integrand becomes:







To find , use u-susbtitution again.

[superflya]

isnt too hard to hard to get the integral of tan(x), bet watchman knows how to do it

rewrite tanx as sinx/cosx

let

now it should look something like this  its in the same form as the 5/x so u know theres gotta be -ln|u|

as u=cosx

u can leave it like that or notice the neg infront of the natural log, u can bring it up to the cos(x)



EDIT: brightskyy

[the.watchman]

I didn't know, but now I do

[TyErd]

So it doesn't matter if we don't know the integral of tan(x)? Will it come up on the exams?

[brightsky]

Nah, not on Methods exams, but it's always handy to know just in case. :p

[TyErd]

okay thanks

[TyErd]

Find , and hence evaluate

Not really sure how to anti differentiate when two terms are multiplied. Btw thats if you can't read it.

[brightsky]

Integrate both sides:







The rest should be straightforward.

EDIT: Forgot the 3 on the RHS :p.

[brightsky]

For a lot of integrals with two terms multiplied together, you can work it out through integration by parts, which the first step (finding the derivative of ) does in a way.

Integration by parts comes from the product rule, just manipulated around. By the product rule:



Integrate both sides:



Manipulate around:



In this case, we let and .