Differentiation is the opposite operation of integration

Here is a question on integration for you to solve:

Phew! Find it difficult?

Here is an interesting method to solve. Hope you enjoy it.

Believe it or not!

We begin with an even more difficult problem:

where t ³ 0

Let

Now, we differentiate F(t) with respect to t.

(In the above, please note that )

Integrate again, we get:

It is not very difficult to find C.

Clearly, F(0) = 0.

This implies that C = 0, and so F(t) = ln(t+1).

Now, we come back to our original integral :

Bingo!