## Calculus 10th Edition

$t+csc(t)+C$
Given: $\int(1-csc(t) cot(t))dt$ Integrate: Integral of $1$ is $t$ Integral of $-csc(t)cot(t)$ is $csc(t)+C$ So $\int(1-csc(t) cot(t))dt=t+csc(t)+C$ Check the result by differentiation: $\frac{d}{dt}(t+csc(t)+C)=1-csc(t)cot(t)$