regroup as tanx (secxtanx)
change tanx to sqrt(sec ² x -1)
use the substitution u = secx ; du =secxtanxdx
see below for more steps
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZHx53BGRjaoT_Bs1i9fl7bqqVfpyS2ih2pySB6BYyIdlgWn1WQtlsWccd5gRHF5-jxgmwafqoA-4yjEt4wWsnzPIcNrDIGoxIW1gHlb_0KSyAA7ruq9saiiLGwJNJXcP35gz3Y60-wW_c/s400/2008-12-05_204651.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrRK2RWptaCHJUDZ8Zm1UDPLIUjCDuuKEO6kdO4jULwq33BgKnpmwiQ0NS10JzfYITY86tDGlQqJd_FE1w8B1FXBOLEYQj5AJ8VqGdCQXZTgVJJ7htfoattnC906FmQGb-DYWHJCC9y00y/s400/2008-12-05_214815.gif)
evaluate integral of { e^(1 /x^2)} / {x^3} -------------(integration by substitution)
evaluate the integral of [e^(-x) +1] ^2 ------------- integration after expansion using identity
integral of e^{x^(1/3)}-------------- e^{x^(1/3)}
integral of x / (x+1)^2-------------integration by adjustment
integrate 1/ (x^7 - x) -----------integration by adjusting
integral of ( ( 4 - x^2 )^( 3/2) ) with limits 0 to 1--------------integration by substitution
integral of [cosx (1+sin²x)] with 0 to π /6 as limits-------------integration by substitution
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