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