i can't seem to figure out how to get this integral.
the integrla of (x+1)/(x^2+2x+2)
the answer is .5ln(x^2+2x+2)+C
Hello, xslim12!
i can't seem to figure out how to get this integral.
. . $\displaystyle \int \frac{(x+1)\,dx}{x^2+2x+2}$
The answer has $\displaystyle \ln$ in it . . . didn't it make you suspicious?
Let: $\displaystyle u \:=\:x^2 + 2x + 2\quad\Rightarrow\quad du \:=\:(2x + 2)\,dx\quad\Rightarrow\quad (x+1)dx \:=\:\frac{1}{2}du$
Substitute: .$\displaystyle \int\frac{\overbrace{(x+1)\,dx}^{\frac{1}{2}\,du}} {\underbrace{x^2+2x+2}_u} \;=\;\frac{1}{2}\int\frac{du}{u} $ . . . . Got it?