What is the integral of sec(x)cot^2(x) ?

The integral of sec(x)cot^2(x) is -csc(x)+C

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integral of sec(x)cot^2(x)

\int sec (x) cot^{2} (x) d x

- csc (x) + C

Solution steps

\int sec (x) cot^{2} (x) d x

Simplify

sec (x) cot^{2} (x) : cot (x) csc (x)

= \int cot (x) csc (x) d x

Apply u-substitution

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = csc (x)

= (- 1) csc (x)

Simplify

= - csc (x)

Add a constant to the solution

= - csc (x) + C

What is the integral of sec(x)cot^2(x) ?
The integral of sec(x)cot^2(x) is -csc(x)+C