How To Integrate sqrt(1-x/1+x)
Published On :2021-01-28 14:00:00
[begin{array}{l} smallint sqrt {frac{{{bf{1}} - x}}{{{bf{1}} + x}}} {rm{d}}x\\ smallint sqrt {frac{{1 - x}}{{1 + x}}} * sqrt {frac{{1 - x}}{{1 - x}}} {rm{d}}x\ smallint frac{{1 - x}}{{sqrt {1 - {x^2}} }}{rm{d}}x\ smallint frac{1}{{sqrt {1 - {x^2}} }}{rm{d}}x - smallint frac{x}{{sqrt {1 - {x^2}} }}{rm{d}}x\ {sin ^{ - 1}}x - smallint frac{x}{{sqrt {1 - {x^2}} }}{rm{d}}x\ By;Substitution;;;\ z = 1 - {x^2};;\ ;;;;;;dz = - 2x;dx\ {sin ^{ - 1}}x + frac{1}{2}smallint frac{1}{{sqrt z }}{rm{d}}z\ {sin ^{ - 1}}x + frac{1}{2}frac{{{{left( z right)}^{frac{1}{2}}}}}{{0.5}} + c\ Rightarrow {sin ^{ - 1}}x + sqrt {1 - {x^2}} + c end{array}]