Solutions - 0040-03

(1) Notice all even powers. Use power-to-frequency conversion:

Plug in:

Simplify:

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(2) Reduce power again for :

(This is derived from the power-to-frequency formula by changing ‘’ to ‘’ in that formula.)

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(3) On the last term, swap even bunch:

Plug all in and obtain:

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(4) Integrate the first three terms:

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(5) Integrate the last term with -sub, setting and :

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(6) Combine in final result:

Note: It is also possible to rewrite using trig identities. So, equally valid answers may look different than this.