Question

Help pleaseyes

Answer 1

\[\int\limits x \log(1+x^{-1})dx=f(x)\log(x+1)+g(x)x^2+Lx+C\]

Answer 2

what do you need help with?

Answer 3

need to find the values of unkown

Answer 4

What grade are you in, so I can get an idea of what to do

Answer 5

@iambatman @rational pls help

Answer 6

I havent done this in years I tried solving but still aint getting the correct answer

Answer 7

I'd say use integration by parts.

Answer 8

thank you so much for a try :)

Answer 9

Are you supposed to prove the left side to the right side?

Answer 10

Your welcome I hope you figure out how to solve this equation!

Answer 11

Oh you mean right side..

Answer 12

well the right hand side is the ans need to figure out the unknown terms

Answer 13

im trying to do

Answer 14

\[\int x\log(1+x^{-1})dx\]\[u = \log(1+x^{-1}) ~,~ du =\frac{1}{1+\frac{1}{x}} \cdot -x^{-2} \implies -\dfrac{\dfrac{1}{x^2}}{\dfrac{x+1}{x}} \implies \text{simplify this...}\]

Answer 15

\[dv=xdx~,~ v = \int xdx = \frac{1}{2}x^2\]`

Answer 16

I don't really know if this will turn out, that was just my guess. I've got to head off OS, so ttyl, and gl.`

Answer 17

look this is what i got @Jhannybean \[= x^2/2\ \log(x+1) - x^2/2\ \ logx + x/2 \ \ -1/2 \\ (\log(1+x)) + C \]

Answer 18

hey i got it @Jhannybean