MHB Integration Sign Error: TI-Nspire Solution

[karush]

View attachment 2106

the bk did not give an answer for this but my TI-nspire gave what is shown,
however I don't know where the - sign (see red arrow) comes from. I looked at the steps given in W|A but thot all the substitution was not needed to solve this.

 

[Opalg]

I agree with you. The $-$ sign should be a $+$. You can tell that the other answer is wrong, because $-\cos x - 1$ is negative and so will not even have a real logarithm.

 

[karush]

ok think I see where I was blind on this

the calculator gave
$\displaystyle
\ln{\left(-\left(\cos{x}-1\right)\right))}
$
which if you distribute the $$-1$$
then $$\ln\left(-\cos(x)+1\right)$$
would be the answer

 

[Krizalid1]

The misuse of the $\implies$ sign is common and makes no sense when writing things like $1+1\implies2.$ It's used when you already stated an equality and want to "imply" some consequence.