Thread: indefinite integral

1. indefinite integral

how does $\frac{x^2}{2}\ln(x^2+1)-\frac{x^2}{2}+\frac{1}{2}\int\frac{2x}{x^2+2}= \frac{1}{2}(x^2+1)\ln(x^2+1)-\frac{x^2}{2}+C$ ??

2. Re: indefinite integral

i know i can proabably do the $\frac{1}{2}\int\frac{2x}{x^2+2}$ part by integration by substitution, letting $x^2+2=t$ and so on, but they seemed to have done it immediately in one step. how?

3. Re: indefinite integral

Originally Posted by muddywaters
how does $\frac{x^2}{2}\ln(x^2+1)-\frac{x^2}{2}+\frac{1}{2}\int\frac{2x}{x^2+2}= \frac{1}{2}(x^2+1)\ln(x^2+1)-\frac{x^2}{2}+C$ ??
$\frac{1}{2}\int {\frac{{2x}}{{{x^2} + 1}}} = \frac{1}{2}\ln \left( {{x^2} + 1} \right)$