What is the integral of (cos(2z))/(cos(z)) ?

The integral of (cos(2z))/(cos(z)) is -ln|tan(z)+sec(z)|+2sin(z)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(2z))/(cos(z))

\int \frac{cos ( 2 z )}{cos ( z )} d z

- ln ∣ tan (z) + sec (z) ∣ + 2 sin (z) + C

Solution steps

\int \frac{cos ( 2 z )}{cos ( z )} d z

Rewrite using trig identities

= \int \frac{- 1 + 2 cos ^{2} ( z )}{cos ( z )} d z

Expand

\frac{- 1 + 2 cos ^{2} ( z )}{cos ( z )} : - \frac{1}{cos ( z )} + 2 cos (z)

= \int - \frac{1}{cos ( z )} + 2 cos (z) d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{1}{cos ( z )} d z + \int 2 cos (z) d z

\int \frac{1}{cos ( z )} d z = ln ∣ tan (z) + sec (z) ∣

\int 2 cos (z) d z = 2 sin (z)

= - ln ∣ tan (z) + sec (z) ∣ + 2 sin (z)

Add a constant to the solution

= - ln ∣ tan (z) + sec (z) ∣ + 2 sin (z) + C

\int \frac{2}{x ( x ^{2} + 2 ) ^{2}} d x

\int arctan (u + 1) d u

\int \frac{cot ( x )}{sin ^{7} ( x ) + 1} d x

\int e sec^{2} (y) d y

\int z^{3} (a^{2} - z^{2})^{\frac{3}{2}} d z

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