12. Trigonometric Functions

Find $g\(\left\)(\(\theta\]\right\))$ by evaluating the following indefinite integral.

$g\(\left\)(\(\theta\[\right\))=\(\int\)^{}\(\left\)(5\(\sec\)^2\(\theta\)-2\(\csc\)^2\(\theta\]\right\))d\(\theta\)$

Find $g\(\left\)(x\(\right\))$ by evaluating the following indefinite integral.

$g\(\left\)(x\(\right\))=\(\int\]\left\)(\(\sin\)^2x-100\(\csc\) x\(\cot\) x+\(\cos\)^2x\(\right\))dx$

Evaluate the indefinite integral.

$\(\int\)_{}^{}\(\theta\]\bullet\) sec^2\(\left\)(5\(\theta\)^2+1\(\right\))d\(\theta\)$

Evaluate the definite integral.

$\(\int\)_{-\(\frac{\pi}{4}\)}^{\(\frac{\pi}{4}\)}\(\tan\) y$ $sec^2ydy$