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.

$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\tan y$ $sec^2ydy$