Find the general indefinite integral. (use c for the constant of integration.) (7θ − 6 csc(θ) cot(θ)) dθ

Answer:[tex]\displaystyle \int {\big[ 7\theta - 6csc(\theta)cot(\theta) \big]} \, d\theta = 6csc(\theta) + \frac{7x^2}{2} + C[/tex]General Formulas and Concepts:CalculusIntegrationIntegrals[Indefinite Integrals] Integration Constant CIntegration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]Step-by-step explanation:Step 1: DefineIdentify[tex]\displaystyle \int {\big[ 7\theta - 6csc(\theta)cot(\theta) \big]} \, d\theta[/tex]Step 2: Integrate[Integral] Rewrite [Integration Property - Addition/Subtraction]:               [tex]\displaystyle \int {\big[ 7\theta - 6csc(\theta)cot(\theta) \big]} \, d\theta = \int {7\theta} \, d\theta - \int {6csc(\theta)cot(\theta)} \, d\theta[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]:               [tex]\displaystyle \int {\big[ 7\theta - 6csc(\theta)cot(\theta) \big]} \, d\theta = 7\int {\theta} \, d\theta - 6\int {csc(\theta)cot(\theta)} \, d\theta[/tex][1st Integral] Reverse Power Rule:                                                               [tex]\displaystyle \int {\big[ 7\theta - 6csc(\theta)cot(\theta) \big]} \, d\theta = 7 \Big( \frac{\theta^2}{2} \Big) - 6\int {csc(\theta)cot(\theta)} \, d\theta[/tex][Integral] Trigonometric Integration:                                                             [tex]\displaystyle \int {\big[ 7\theta - 6csc(\theta)cot(\theta) \big]} \, d\theta = 7 \Big( \frac{\theta^2}{2} \Big) - 6[-csc(\theta)] + C[/tex]Simplify:                                                                                                         [tex]\displaystyle \int {\big[ 7\theta - 6csc(\theta)cot(\theta) \big]} \, d\theta = 6csc(\theta) + \frac{7x^2}{2} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)Unit:  Integration