Acinod's Question Thread

[acinod]

Without using integration by parts or recognition and showing full working, integrate the following:

• ln(x)
• xcos(x)

Let u=tan(x/2), -pi<x<pi. Find sin(x) and cos(x) as a rational expression of u only without using any trigonometry notations.

[dcc]

Code: (Mathematica Output) [Select]

In[8]:= Integrate[Log[x], x]
Out[8]= -x + x Log[x]

In[9]:= Integrate[x*Cos[x], x]
Out[9]= Cos[x] + x Sin[x]

[acinod]

Code: (Mathematica Output) [Select]

In[8]:= Integrate[Log[x], x]
Out[8]= -x + x Log[x]

In[9]:= Integrate[x*Cos[x], x]
Out[9]= Cos[x] + x Sin[x]

Oops sorry I forgot to mention, full working required.

[dcc]

The full working was provided.

[acinod]

The full working was provided.

Wow after staring at the working for a couple of minutes, I finally understood what you did there. Actually I'm still a bit confused but I get the general idea.
Is there another way to do this? Like using only the knowledge learnt in the Year 12 course?

[dcc]

Back in my day, this was part of the Year 12 course.