"I love how grant actually gets irritated and starts bullying cot sec and cosec<br><br><a href=""https://www.youtube.com/watch?v=amCsM265Lw0&amp;t=4m45s"">4:45</a>",(reply>), Whats the derivative of tanx😈,(reply>), @YEO Consider this expansion of π...<br>π ≈<br>3×<br>(sec(π÷12))<br>×(sec(π÷24))<br>×(sec(π÷48))<br>×(sec(π÷96))<br>×(sec(π÷192))<br>×...,(reply>), @Quantum Diaming Consider this expansion of π...<br>π ≈<br>3×<br>(sec(π÷12))<br>×(sec(π÷24))<br>×(sec(π÷48))<br>×(sec(π÷96))<br>×(sec(π÷192))<br>×...,(reply>), I support those brave words,(reply>), @Farmer kun arcsec not needed. Again "tan" is only needed, or arctan in this case.<br><br>let u = sqrt(x^2-1)<br>u^2 = x^2 - 1<br>x^2 = u^2 + 1<br>2xdx = 2udu<br>dx = udu/x <br><br>integral of 1/(xsqrt(x^2-1)) dx = integral of 1/(xu) * (u/x) du<br>                                                = integral of 1/x^2 du<br>                                                = integral of 1/(u^2 + 1) du<br>                                                = arctan(u) + C<br>                                                = arctan(sqrt(x^2-1)) + C<br><br>In fact, arcsec is a bit messy since you need either the sgn(x) function or |x|/x<br>as integral of 1/(xsqrt(x^2-1)) dx = |x|arcsec(x)/x, but arctan doesn't need any sgn(x) function or something similar. the primitive is simply arctan(sqrt(x^2-1)) + C