Must I complete the square of the denominator? If so, after completing the square my answer is (x+1)^2 + (1/2).
I then set a to be sqrt(1/2) and u to be x+1, which means dx = du. Is this right so far.
Can someone rotate this picture for easy reading?
Where did the 1/2 in front of the fraction come from?
Is 1-4x-2x^2 the same when written
-2x^2-4x+1? This is what I assumed the original denominator to be by simply rearranging the terms before completing the square. Are you saying that I completed the square wrongly? Good night. I will check your reply in the morning.
romsek,
I let a = sqrt(3/2) which can be written as sqrt(6)/2. I let u be x+1, which means
dx = du. When I plug those values into the formula in the picture, my answer is the following:
[1/sqrt(6) * ln |[sqrt(6)/2] + x+1]/sqrt(6)/2 - (x-1)] + C.
What am I doing wrong?
I see what happened. I divided across by -2 when I should have factored out a 2 instead. By factoring out 2, the numerator being 1, there is my factor 1/2 in front. Great work, romsek.
Tomorrow I begin learning how to find the area between two curves. Try to understand that I am learning calculus material outside a classroom setting. I hope you do not think I am nuts but math has been my passion for many years.
I am 48 years old. It makes zero sense to take out a school loan for the purpose of majoring in math at this late stage in my life. But, we are never too old to do a self-study of any topic, right? What is your input in terms of learning just to know how to do something?
romsek,
Thanks. Yes, math helps me to continue paying attention to detail. My job has nothing to do with math. I have two CUNY degrees in areas other than math. I took precalculus in 1993 and got an A minus. I should have continued in math but made a wrong a choice. I also have an online degree in Religious Education with concentration on eschatology. My friends and family see no purpose in studying calculus because they say it is not practical. They say I will never be James Stewart. I am not trying to be James Stewart. I just love math as crazy as that sounds. I am divorced. I am not popular with the ladies. So, why not learn math, right?
romsek,
I did the algebra and still got the wrong answer. My answer:
1/(2*sqrt{6}) ln |sqrt(6)/2 + (x+1) divided by sqrt(6)/2 - (x+1)| + C
I give up here. Can you finish this question in steps? It will help me as a guide for future similar questions.