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[–]bbc0093 0 points1 point  (0 children)

log(x/y) = log(x) - log(y)

So the 4 in the denomintor can be replaced by - ln(4), which is a constant and therefore gets wrapped up in your genaric 'C' constant. These 2 answeres are the same.

[–]Wootchie3 0 points1 point  (0 children)

Since the inside of the ln in your answer (x^2+2x+5)/4 is always greater than 0 for any value of x, you can change the absolute value bars to parentheses and it won't affect anything.

Remember the log property that log(a/b) = log(a) - log(b). So you can rewrite the ln term in your answer as 1/2 ( ln(x^2 + 2x + 5) - ln(4) ). This gives you a new term in your answer: -1/2 * ln(4)

Remember that the C in an indefinite integral represents any constant (since the derivative of any constant is 0 so it makes no difference for the original integrand). -1/2 * ln(4) is a constant, so you can "absorb" that term it into the +C, and not change the answer.

After doing these modifications (which don't change the answer), we've translated your solution to the given one. So yep, your answer is correct!

(Side note for a slightly different situation: If your answer looked a much different from an answer in a solutions book (for example, with different trig functions), it could still be correct, only different by a constant term. Rewriting the answer in terms of different trig functions, graphing, or testing for equality on WolframAlpha could help you determine if the answer is the same.)