QUESTION $10$

Evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{(-sint-7)costdt}{si{n}^{3}t+2si{n}^{2}t+sint+2}$

a$.-ln|t+2|+\frac{1}{2}ln|t^2+1|-3ta{n}^{-1}t+C$

b$.-ln|sint+2|+\frac{1}{2}ln|si{n}^{2}t+1|-3ta{n}^{-1}(sint)+C$

c$.$ In $|sint+2|-ln|si{n}^{2}t+1|-5ta{n}^{-1}(sint)+C$

d$.-ln|sint+2|+\frac{1}{2}ln|si{n}^{2}t+1|+C$