How To Integrate sec^4(x)tan^3(x)
Published On :2020-12-06 20:36:00
[begin{array}{l} smallint se{c^{bf{4}}}xta{n^{bf{3}}}x{rm{d}}x\\ smallint {sec ^2}{rm{x}}{tan ^3}{rm{x}}{sec ^2}{rm{xdx}}\ smallint left( {1 + {{tan }^2}x} right){tan ^3};x{sec ^2}x{rm{d}}x\ By;Substitution;;;;;\ ;;;;;;;;;;;;;;;;Suppose Rightarrow z = tan x\ ;;;;;;;;;;;;;dz = {sec ^2}x;;dx\\ smallint left( {1 + {z^2}} right){z^3}{rm{d}}z\ smallint {z^5} + {z^3}{rm{d}}z\ Rightarrow frac{{{z^6}}}{6} + frac{{{z^4}}}{4} + c\ Rightarrow frac{{{{tan }^6}x}}{6} + frac{{{{tan }^4}x}}{4} + c end{array}]