Solutions - 0050-02

(1) Trig substitution. Notice , so we should make use of the identity .

Pick and thus .

Then:

Plug in:

(We assume that for the relevant values of .)

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(2) Perform integration.

Either recall from memory, or multiply above and below by , and obtain:

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(3) To convert to we need given that .

Draw triangle expressing :

Therefore . We already know . Thus:

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(4) Simplify with log rules: