Trignometric integral : ∫ d x sin ⁡ x + sec ⁡ x

Question

Trignometric integral :   ∫            d      x              sin      ⁡      x      +      sec      ⁡      x

floygdarvn · Accepted Answer

look at this way:                    2        cos        ⁡        x                    2        +        2        cos        ⁡        x        sin        ⁡        x              =                    cos        ⁡        x        −        sin        ⁡        x                    2        +        2        cos        ⁡        x        sin        ⁡        x              +                    cos        ⁡        x        +        sin        ⁡        x                    2        +        2        cos        ⁡        x        sin        ⁡        x            As       ∫    (    cos    ⁡    x    −    sin    ⁡    x    )    d    x    =    cos    ⁡    x    +    sin    ⁡    x    ,  , write   2  cos  ⁡  x  sin  ⁡  x  =  (  cos  ⁡  x  +  sin  ⁡  x      )    2    −  1 and set   cos  ⁡  x  +  sin  ⁡  x  =  uand as       ∫    (    cos    ⁡    x    +    sin    ⁡    x    )    d    x    =    sin    ⁡    x    −    cos    ⁡    x    ,  , write   2  cos  ⁡  x  sin  ⁡  x  =  1  −  (  sin  ⁡  x  −  cos  ⁡  x      )    2   and set   sin  ⁡  x  −  cos  ⁡  x  =  v

Trignometric integral : ∫ d x </mrow>

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