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Integrate the following functions: tan^4...

Integrate the following functions: `tan^4x`

Text Solution

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`tan^4x = tan^2 x tan^2 x`
=`tan^2 x sec^2 x-(sec^2 x-1)`
=`tan^2 x sec^2 x -sec^2 x+1`
therefore `int tan^4 x dx`
=`int (ta_n^2x sec^2 x-sec^2 x+1)dx`
`int t^2dt-tanx+x+c`, if we put
tanx =t
=`t^3/3-tanx+x+c`
=`tan^3 x/3 -tanx+x+c`
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