Question

Evaluate the integral of: 1 / (x^2 * sqrt(x^2 + 16))?

I used the substitution x = 4 * tan t, but i couldnt work out the answer. Can someone please enlighten me?

Answer 1

Step 1:

The integral is .

Consider .

Substitute and in the integral.

                                

From basic integration formulas : .

                                

From

From Pythagorean theorem,

Substitute in the above expression.

                                  

Solution :

.