Question
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
Solution
4.6
(199 Votes)
Shaw
Professional ยท Tutor for 6 years
Answer
### straight-forward u-substitution
Explanation
## Step 1: Analyze the integral### The integral
involves
and
. The derivative of
is
. This suggests a u-substitution with
.## Step 2: Perform u-substitution### Let
. Then
. The integral becomes
.## Step 3: Evaluate the integral###
.## Step 4: Substitute back### Substituting back
, we get
.