What is the integral of (sec^3(x))/(tan^2(x)) ?

The integral of (sec^3(x))/(tan^2(x)) is -csc(x)+ln|tan(x)+sec(x)|+C

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integral of (sec^3(x))/(tan^2(x))

\int \frac{sec ^{3} ( x )}{tan ^{2} ( x )} d x

- csc (x) + ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{sec ^{3} ( x )}{tan ^{2} ( x )} d x

Rewrite using trig identities

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

Apply Integration By Parts

: - csc (x) - \int - sec (x) d x

= - csc (x) - \int - sec (x) d x

\int - sec (x) d x = - ln ∣ tan (x) + sec (x) ∣

= - csc (x) - (- ln ∣ tan (x) + sec (x) ∣)

Simplify

= - csc (x) + ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= - csc (x) + ln ∣ tan (x) + sec (x) ∣ + C

\frac{\partial}{\partial x} (16 x + 32 y - 1600)

\frac{x}{x + 1}

n = 0 \sum \infty \frac{1}{n ^{3} - n}

\int \frac{1}{x ^{3} - 4 x ^{2} + 3 x} d x

\int 4 x (x^{2} + 5)^{3} d x

What is the integral of (sec^3(x))/(tan^2(x)) ?
The integral of (sec^3(x))/(tan^2(x)) is -csc(x)+ln|tan(x)+sec(x)|+C