# How proof this answer is right ? ∫ ((1)/((x^2)(sqrt(1+x^2))dx =

##### 3 Answers

#### Explanation:

Clear image of the equation

Show that the derivative of what you think is the answer is the integrand in the original problem.

#### Explanation:

Quick example:

To prove that

In your question, show that the derivative of

It is clear that we can ignore the

You could do the actual integral and check each step along the way.

Let:

This is a typical trig substitution strategy and is verified in any calculus textbook that teaches this. You can check the

Therefore you get:

Using identities

Some u-substitution can be done now as well. Let:

That is our temporary answer. Finally, going back to the original substitution of

Therefore the final answer is indeed: