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Math Help - solve a integral without using without using trigo-substitution?

  1. #1
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    solve a integral without using without using trigo-substitution?

    solve a integral without using without using trigo-substitution?
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  2. #2
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    Sure! Look it up in a table.

    Really, my first question would be, "Why?"
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  3. #3
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    Both of those are in arctangent form.
    Look at the derivative of the arctangent(x).
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  4. #4
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    I think it's an useless question, 'cause it's an immediate integral.

    But you can say y=\arctan x\implies\tan y=x\,\therefore\,y'(1+x^2)=1.

    So, y'=\frac1{1+x^2}.

    Now integrate both sides y+k=\int\frac1{1+x^2}\,dx.

    Since y=\arctan x, we happily get that \arctan x+k=\int\frac1{1+x^2}\,dx.
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