Evaluate dx / ^ 9-8x - x2^ a. ln (-8 - 2x) + c b. sin -1 (x+4/5) + c c. sin -1 (x-4/5) + c d. ln ^ 9-8x-x2^ + c my apologies if i wrote it out a little wrong and you can’t understand! hopefully i did it right

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for .

In that case, you want to find the antiderivative,



Complete the square in the denominator:



Now substitute , so that . Then



which simplifies to



Now, recall that . But we want the substitution we made to be reversible, so that



which implies that . (This is the range of the inverse sine function.)

Under these conditions, we have , which lets us reduce . Finally,



and back-substituting to get this in terms of yields