7. Antiderivatives & Indefinite Integrals

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 integral: ${\int }_{}^{}\arctan \left(\frac{1}{x}\right)dx$

Evaluate the integral: ${\int }_1^7{w}^2\ln \left(w\right) dw$