Integrating 1/sqrt(x^2+16): Common Mistakes and Correct Solution

[albireo]

Homework Statement

Integrate 1/sqrt(x^2+16)


The answer I get is :
ln ((sqrt(16+x^2)+x)/4)+C

and it is incorrect. The answer is ln(sqrt(16+x^2)+x) + C

 

[gabbagabbahey]

Hint:

$$ln(a/b)=ln(a)-ln(b)$$

 

[albireo]

but ln4 is not =0

 

[gabbagabbahey]

No, but $$C- ln(4)$$ is still just a constant. Basically, your solution is correct but it is also equivalent to the other solution just with a different value of $$C$$.

 

[albireo]

Of course! Thanks a lot:)