How to find the integral of sin 3 [ x ] d x ?

Question

How to find the integral of                     sin        3                    [        x        ]                    d      x      ?

unieventos8l9 · Accepted Answer

∫                  sin        3                    (        x        )                    d      x        =    ∫          sin              (        x        )                    (      1      -                        cos          2                          (          x          )                    )              d      x            =    ∫          sin              (        x        )                    d      x        -    ∫          sin              (        x        )                            cos        2                    (        x        )                    d      x      For the first integral:      ∫          sin              (        x        )                    d      x        =    -          cos              (        x        )              +    C  Using substitution, compute the second integral as follows:Let       u    =          cos              (        x        )              ⇒    d    u    =    -          sin              (        x        )                    d      x      Then      -    ∫          sin              (        x        )                            cos        2                    (        x        )                    d      x        =    ∫          u      2        d    u        =                  u        3            3        +    C        =          1      3                      cos        3                    (        x        )              +    C  Putting it all together, we get our final result:      ∫                  sin        3                    (        x        )                    d      x        =    ∫          sin              (        x        )                    d      x        -    ∫          sin              (        x        )                            cos        2                    (        x        )                    d      x            =    -          cos              (        x        )              +          1      3                      cos        3                    (        x        )              +    C

How to find the integral of sin 3 [ x ] d x ?

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