Calculate integral y = (tgx+(tgx)^3), 0<x<pie/2

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aruv | High School Teacher | (Level 2) Valedictorian

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Problem is to find

`int_0^(pi/2)(tan(x)+tan^3(x))dx=int_0^(pi/2)(tan(x)(1+tan^2(x)))dx`

`=int_0^(pi/2)tan(x)sec^2(x)dx`

`Let`

`tan(x)=t`

`sec^2(x)dx=dt`

`int tan(x)sec^2(x)dx=inttdt=t^2/2=(tan^2(x))/2`

Thus

`int_0^(pi/2)(tan(x)sec^2(x))dx=(tan^2(x))/2|_0^(pi/2)=oo`

`Thus`

integral of y is infinite.

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