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Math Help - indefinite integral

  1. #1
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    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 ??
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  2. #2
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    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?
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  3. #3
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    Re: indefinite integral

    Quote Originally Posted by muddywaters View Post
    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)
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