What is the integral of (sec(θ))/(tan^2(θ)) ?

The integral of (sec(θ))/(tan^2(θ)) is -csc(θ)+C

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integral of (sec(θ))/(tan^2(θ))

\int \frac{sec ( θ )}{tan ^{2} ( θ )} d θ

- csc (θ) + C

Solution steps

\int \frac{sec ( θ )}{tan ^{2} ( θ )} d θ

Rewrite using trig identities

= \int \frac{cos ( θ )}{sin ^{2} ( θ )} d θ

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = sin (θ)

= - \frac{1}{sin ( θ )}

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= - csc (θ)

Add a constant to the solution

= - csc (θ) + C

\frac{d}{d θ} (cot^{2} (cos (θ)))

\frac{x + 1 - 3}{x - 8}

\int 2 x^{\frac{1}{2}} d x

\int_{0}^{\frac{π}{2}} 2 cos^{5} (x) d x

\frac{\partial}{\partial x} (x^{a})

What is the integral of (sec(θ))/(tan^2(θ)) ?
The integral of (sec(θ))/(tan^2(θ)) is -csc(θ)+C