text: You have to use substitution.\n\nLet u = cos(x)\ndu = -sin(x) dx, so\n-du = sin(x)dx\n\nTherefore, your new integral becomes:\n\n-1 / (1 + u^2)\n\nAnd integrating that, you get \n- tan(inverse) (u)\n\nResubstituting u=cos(x), you get\n\n-tan(inverse) (cos(x))