Are these two antiderivatives equivalent?Regarding the anti derivative of: cos 3 ⁡ ( x ) sin 3 ⁡ ( x ) Is the answer − sin 4 ⁡ ( x ) ( 2 sin 2 ⁡ ( x ) − 3 ) 12 equivalent to sin 4 ⁡ ( x ) 4 .If so, how? Integral Calculator says they're equivalent, but I don't understand how.

Question

Are these two antiderivatives equivalent?Regarding the anti derivative of:       cos    3    ⁡      (    x    )        sin    3    ⁡      (    x    )  Is the answer   −                              sin          4                ⁡                  (          x          )                          (          2                      sin            2                    ⁡                      (            x            )                    −          3          )                    12       equivalent to                               sin          4                ⁡                  (          x          )                    4      .If so, how? Integral Calculator says they&#039;re equivalent, but I don&#039;t understand how.

Punktatsp · Accepted Answer

Explanation:The first function is indeed an antiderivatives of       cos    3    ⁡  (  x  )      sin    3    ⁡  (  x  ). But if you differentiate the second one, what you get is   cos  ⁡  (  x  )      sin    3    ⁡  (  x  ), rather than       cos    3    ⁡  (  x  )      sin    3    ⁡  (  x  ).

arridsd9 · Accepted Answer

Explanation:If both are antiderivatives of the same function, then their difference will be constant.But their difference is   −                              sin          6                ⁡        x            6       which is not constant.

Are these two antiderivatives equivalent? Regarding the anti derivative of: cos 3 </m

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