Question

What is the solution of Integral :

(x²+4x)/sqrt(x²+2x+2)

Do not use an integral calculator, please help !!

Answer 1

Do you know how to integrate by first using a trig sub?

Answer 2

Try to write the thing in the radical as a sum of squares and pick your trig sub based on that.
Let me know what you choose it to be.

Answer 3

hint:
\[\Large \cosh^2 \alpha-\sinh^2\alpha=1\]
The hyperbolic trigonometric Pythagoras. Hopefully it will make your life a bit easier after completing the square.