I believe there was an error made in the second problem since you wrote down -4 at one part when you said plus 4 so the final answer is as far as i can tell not correct.
You could make #2 a lot simpler by separating the parts of your numerator prior to the back sub for the x^2, making it a lot simpler, and less confusing to come away with 1/2u^2-4u+8lnu.
WHAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAATTTTTTTTTTTTTTTTTTTTTTTTTTTTT MY JAW DROPPED THATS SO COOL
Found the correct answer for the original problem I think: S( (x^2 +4) / (x+2) dx ) = (x^2)/2 - 2x - 6 + 8*Ln(x+2) + C let u = x+2 --> x = u-2 --> du=dx, S( (x^2 + 4)/(x+2) dx) = S( ( (u-2)^2 +4 )/u du ) = S( (u^2 -4u +4 +4)/u du ) =S( (u^2 -4u +8)*u^-1 du ) = S( u - 4 + 8 (1/u) du ) S( u^2 du ) - S (4 du ) + 8*S( 1/u du) = (u^2)/2 - 4u +8(Ln(u)) + C = ( (x+2)^2)/2 - 4(x+2) + 8*Ln(x+2) + C = (x^2 +4x +4)/2 - 4x - 8 + 8*ln(x+2) + C = (x^2)/2 +2x +2 -4x -8 +8*ln(x+2) + C = (x^2)/2 -2x -6 + 8*ln(x+2) + C Kinda hard to read on a comments sections with no math symbols but hopefully one can read it.
I believe there was an error made in the second problem since you wrote down -4 at one part when you said plus 4 so the final answer is as far as i can tell not correct.
Agreed, good catch!
Yep there is error in last part of second question... 😊
Yeah I was just thinking why does 4 change to -4, tnx for pointing it out
@@Lukav1 dudes having a conversation over the past half decade
@@sizzle9324 Yeah 😂
You could make #2 a lot simpler by separating the parts of your numerator prior to the back sub for the x^2, making it a lot simpler, and less confusing to come away with 1/2u^2-4u+8lnu.
WHAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAATTTTTTTTTTTTTTTTTTTTTTTTTTTTT MY JAW DROPPED THATS SO COOL
Found the correct answer for the original problem I think:
S( (x^2 +4) / (x+2) dx ) = (x^2)/2 - 2x - 6 + 8*Ln(x+2) + C
let u = x+2 --> x = u-2 --> du=dx,
S( (x^2 + 4)/(x+2) dx) = S( ( (u-2)^2 +4 )/u du ) = S( (u^2 -4u +4 +4)/u du )
=S( (u^2 -4u +8)*u^-1 du ) = S( u - 4 + 8 (1/u) du )
S( u^2 du ) - S (4 du ) + 8*S( 1/u du) = (u^2)/2 - 4u +8(Ln(u)) + C
= ( (x+2)^2)/2 - 4(x+2) + 8*Ln(x+2) + C = (x^2 +4x +4)/2 - 4x - 8 + 8*ln(x+2) + C
= (x^2)/2 +2x +2 -4x -8 +8*ln(x+2) + C = (x^2)/2 -2x -6 + 8*ln(x+2) + C
Kinda hard to read on a comments sections with no math symbols but hopefully one can read it.
sigma