What is the integral of (sec(2y)tan(2y))/(4+sec(2y)) ?

The integral of (sec(2y)tan(2y))/(4+sec(2y)) is 1/2 ln|4+sec(2y)|+C

Popular >

integral of (sec(2y)tan(2y))/(4+sec(2y))

\int \frac{sec ( 2 y ) tan ( 2 y )}{4 + sec ( 2 y )} d y

\frac{1}{2} ln ∣ 4 + sec (2 y) ∣ + C

Solution steps

\int \frac{sec ( 2 y ) tan ( 2 y )}{4 + sec ( 2 y )} d y

Apply u-substitution

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = 4 + sec (2 y)

= \frac{1}{2} ln ∣ 4 + sec (2 y) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ 4 + sec (2 y) ∣ + C

- 2 x^{4} + 7 x e^{3 x - 2}

\int_{1}^{\infty} ln (x) d x

\frac{\partial}{\partial x} (\frac{t x ( 1 - x )}{1 - t ^{2}})

\int (\frac{e ^{\frac{1}{x}}}{x ^{2}}) d x

\int \frac{( 10 x + 2 )}{( 3 x + 1 ) ( x - 1 )} d x

What is the integral of (sec(2y)tan(2y))/(4+sec(2y)) ?
The integral of (sec(2y)tan(2y))/(4+sec(2y)) is 1/2 ln|4+sec(2y)|+C