$$\Huge \int x \sin (x) \text{d}x $$

Question

geerky42 · Answer

@Callisto @CliffSedge 

Any idea?

anonymous · Answer

I'd use integration by parts.

geerky42 · Answer

How? Sorry, I'm new to integral...

anonymous · Answer

If you've never heard of integration by parts, then this is going to be a long lesson.
Are you familiar with the product rule for differentiation?

geerky42 · Answer

Yes, I'm familiar with product rule.

geerky42 · Answer

I don't see what it has to do with integral, lol.

anonymous · Answer

By the Fundamental Theorem of Calculus, integration is the inverse of differentiation.
It would be the same as if you had a logarithm problem, and I asked if you knew how to handle exponents.

anonymous · Answer

Integration by parts is derived from the product rule.

geerky42 · Answer

Wait...  do you mean we have to "solve inversely" or something like this? 

I'm not sure what you mean.

anonymous · Answer

Take (uv)' = uv' + vu' and rewrite as uv' = (uv)' - vu' and integrate both sides.
You'll get $$\large \int\limits udv=uv-\int\limits vdu$$

anonymous · Answer

In your example, let u=x and dv=sin(x)dx.

anonymous · Answer

Can you get it from there, @geerky42 ?

geerky42 · Answer

Yes, I can. Thanks.