Can I get a hint on how to integrate 1 + sin 2 ⁡ xI'm working on a line integral problem and have simplified to the integrand ( 1 + sin 2 ⁡ θ ) d θWhat can I do from here?

Question

Can I get a hint on how to integrate   1  +      sin    2    ⁡  xI&#039;m working on a line integral problem and have simplified to the integrand  (  1  +      sin    2    ⁡  θ  )  d  θWhat can I do from here?

Judovh0 · Accepted Answer

Alternatively, you can use integration by parts:   ∫      sin    2    ⁡  (  x  )  d  x  =  ∫  sin  ⁡  (  x  )  sin  ⁡  (  x  )  d  xNow remember that   ∫  a  ⋅      b    ′    =  a  ⋅  b  −  ∫      a    ′    ⋅  b and       sin    2    +      cos    2    =  1

Celia Lucas · Accepted Answer

Notice,  ∫  (  1  +      sin    2    ⁡  x  )  d  x  =  ∫      (    1    +                  1        −        cos        ⁡        2        x            2        )    d  x  =  ∫      (          3      2        −                  cos        ⁡        2        x            2        )    d  x  =      3    2    ∫     d  x  +      1    4    ∫  cos  ⁡  2  x     d  (  2  x  )

Can I get a hint on how to integrate 1 + sin 2 </msup> ⁡

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