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

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

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integral of (sec(x))/(tan^2(x))

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

- csc (x) + C

Solution steps

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

Rewrite using trig identities

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

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 (x)

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

Use the basic trigonometric identity:

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

= - csc (x)

Add a constant to the solution

= - csc (x) + C

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