Which of the following methods is most efficient for evaluating the integral: int cot4(x)csc^2(x)dx Select only ONE answer straight-forward u-substitution using trig integration (with the identity csc^2(x)=cot^2(x)-1) Ore-write everything in terms of sine and cosine using trig integration (by first splitting up the integrand as cot^3(x)csc(x)cot(x)csc(x) , and then using the appropriate trig identity

## Step 1: Analyze the integral<br />### The integral $\int \cot^4(x)\csc^2(x)dx$ involves $\cot(x)$ and $\csc(x)$. The derivative of $\cot(x)$ is $-\csc^2(x)$. This suggests a u-substitution with $u = \cot(x)$.<br /><br />## Step 2: Perform u-substitution<br />### Let $u = \cot(x)$. Then $du = -\csc^2(x) dx$. The integral becomes $\int u^4 (-du) = -\int u^4 du$.<br /><br />## Step 3: Evaluate the integral<br />### $-\int u^4 du = -\frac{u^5}{5} + C$.<br /><br />## Step 4: Substitute back<br />### Substituting back $u = \cot(x)$, we get $-\frac{\cot^5(x)}{5} + C$.