Integrate 1÷(1 + cosec x ) ?

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Answer 1 · 2018-04-04T06:50:17

#int1/(1+cscx)dx=secx-tanx+x+c#

#int1/(1+cscx)dx#

= #int(cscx-1)/((cscx-1)(cscx+1))dx#

= #int(cscx-1)/(csc^2x-1)dx#

= #int(cscx-1)/cot^2xdx#

= #int(sin^2x/(sinxcos^2x)-tan^2x)dx#

= #int(sinx/cos^2x-sec^2x+1)dx#

= #int(secxtanx-sec^2x+1)dx#

= #secx-tanx+x+c#

Answer 2 · 2018-04-04T06:50:39

#int1/(1 + cosec x )#

#=int1/(1 + 1/sin x )#

#=intsin x /(sin x + 1)#

#=int(sin x(sin x - 1)) /((sin x + 1)(sin x - 1))#

#=int(sinx-sin^2x)/(cos^2x)dx#

#=inttanxsecxdx-inttan^2xdx#

#=inttanxsecxdx-int (sec^2x-1)dx#

#=secx-(tanx-x)+c#

#=x+secx-tanx+c#