What is the integral of ((1-sin^2(x)))/(cos^3(x)) ?

The integral of ((1-sin^2(x)))/(cos^3(x)) is ln|tan(x)+sec(x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((1-sin^2(x)))/(cos^3(x))

\int \frac{( 1 - sin ^{2} ( x ) )}{cos ^{3} ( x )} d x

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{1 - sin ^{2} ( x )}{cos ^{3} ( x )} d x

Rewrite using trig identities

= \int sec (x) d x

Use the common integral:

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

= ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ + C

\int cot^{5} (6 x) csc^{7} (6 x) d x

\int x^{3} e^{n x} d x

\int 2 x (x^{2} - 3) d x

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

\int sin^{3} (\frac{x}{2}) cos^{3} (\frac{x}{2}) d x

What is the integral of ((1-sin^2(x)))/(cos^3(x)) ?
The integral of ((1-sin^2(x)))/(cos^3(x)) is ln|tan(x)+sec(x)|+C