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

Evaluating integrals Evaluate the following integrals.                                                                                                                                      

 ∫ 𝓍² cos 𝓍³ d𝓍

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ (cos 7ω) /(16 + sin² 7ω) dω 

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫(√1 + tan 2t) sec² 2t dt

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ sin 𝒵 sin (cos 𝒵) d𝒵