Running into a little trouble when doing this integral by hand:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int arccsc(x) dx [/tex]

[tex] u = arccsc(x) \implies du = -\frac{1}{x\sqrt{x^{2}-1}} dx[/tex]

[tex] dv = dx \implies v = x [/tex]

[tex] \int u dv = uv - \int vdu [/tex]

[tex] \int arccsc(x) dx = xarccsc(x) - \int x\cdot -\frac{1}{x\sqrt{x^{2}-1}} dx [/tex]

[tex] \int arccsc(x) dx = xarccsc(x) + \int \frac{1}{\sqrt{x^{2}-1}} dx [/tex]

Now I'm here, and it seems obvious , but this yields the answer to be:

[tex] \int arccsc(x) dx = xarccsc(x) + \ln\left|\sqrt{x^{2}-1}\right| +C [/tex]

When it's suppose to be (from wikipedia):

[tex] \int arccsc(x) dx = xarccsc(x) + \ln\left(x+\sqrt{x^{2}-1}\right) +C [/tex]

Where did I go wrong (skipped ahead in the course, so sorry if it's something really basic I'm missing)?

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# Integral of Inverse Cosecant

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