Home > Calculus > Integrals of Trigonometric Functions

How do you integrate #1/tan(x) dx#?

Answer 1

Aurora Alvarado

#int 1/tan x dx = ln abs(sin x) + C#

Note that:

#int 1/t dt = ln abs(t) + C#

So we find:

#int 1/tan x dx = int cos x/sin x dx#

#color(white)(int 1/tan x dx) = int (d/dx sin x)*1/sin x dx#

#color(white)(int 1/tan x dx) = ln abs(sin x) + C#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emily Ammerman

#int dx/tanx = int cosx/sinx dx = int (d(sinx))/sinx = ln abs (sinx)+ C#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Paisley Johnson

To integrate 1/tan(x) dx, you can use the trigonometric identity: 1/tan(x) = cos(x)/sin(x). Then, rewrite the integral as ∫cos(x)/sin(x) dx. Next, perform substitution: Let u = sin(x), then du = cos(x) dx. The integral becomes ∫du/u, which integrates to ln|u| + C. Substitute back sin(x) for u, yielding ln|sin(x)| + C. Therefore, the integral of 1/tan(x) dx is ln|sin(x)| + C.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.