Question

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

Answer 1

$\int \! 70 - 6 \csc(\theta) \cot(\theta) \ \mathrm{d}\theta = \int \! 70 - 6 \cdot \frac{1}{\sin(\theta)} \cdot \frac{\cos(\theta)}{\sin(\theta)} \ \mathrm{d}\theta = \int \! 70 \ \mathrm{d}\theta - \int \! \frac{6 \cos(\theta)}{\sin^2(\theta)} \ \mathrm{d}\theta = 70 \theta + \frac{6}{\sin(\theta)} + C, \ C \in \mathbb{R}.$