Thread: Finding the indefinite integral

⌠
⌡ cot^2(x) dx

I approached this question by replacing cot^2 (x) w/ [cos^2(x)]/[sin^2(x)] => substituting sin^2(x) w/ u^2 => and ended up w/ -(1/3)cot(x) csc^2(x) + C

The answer key just gives -cot (x) - x + C

I have no idea of drawing any correlation so far except I didnt approach the trig sign from the correct position to begin with. Help with detailed algebraic work to this answer is what I ask please.

Originally Posted by ugkwan

⌠
⌡ cot^2(x) dx

I approached this question by replacing cot^2 (x) w/ [cos^2(x)]/[sin^2(x)] => substituting sin^2(x) w/ u^2 => and ended up w/ -(1/3)cot(x) csc^2(x) + C

The answer key just gives -cot (x) - x + C

I have no idea of drawing any correlation so far except I didnt approach the trig sign from the correct position to begin with. Help with detailed algebraic work to this answer is what I ask please.

From the Pythagorean Identity: .

And since the derivative of is ....

Originally Posted by ugkwan

⌠
⌡ cot^2(x) dx

I approached this question by replacing cot^2 (x) w/ [cos^2(x)]/[sin^2(x)] => substituting sin^2(x) w/ u^2 => and ended up w/ -(1/3)cot(x) csc^2(x) + C

If you let , then and . Now you have two "cosines" in the problem so you will have and you still have that "cos(x)" in the integral. You could then argue that and so change the integral to but I don't that that's any easier!

The answer key just gives -cot (x) - x + C

I have no idea of drawing any correlation so far except I didnt approach the trig sign from the correct position to begin with. Help with detailed algebraic work to this answer is what I ask please.[/QUOTE]