What is the integral of 4sec^2(4x-2) ?

The integral of 4sec^2(4x-2) is tan(4x-2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4sec^2(4x-2)

\int 4 sec^{2} (4 x - 2) d x

tan (4 x - 2) + C

Solution steps

\int 4 sec^{2} (4 x - 2) d x

Take the constant out:

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

= 4 \cdot \int sec^{2} (4 x - 2) d x

Apply u-substitution

: \int sec^{2} (u) \frac{1}{4} d u

= 4 \cdot \int sec^{2} (u) \frac{1}{4} d u

Take the constant out:

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

= 4 \cdot \frac{1}{4} \cdot \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= 4 \cdot \frac{1}{4} tan (u)

Substitute back

u = 4 x - 2

= 4 \cdot \frac{1}{4} tan (4 x - 2)

Simplify

4 \cdot \frac{1}{4} tan (4 x - 2) : tan (4 x - 2)

= tan (4 x - 2)

Add a constant to the solution

= tan (4 x - 2) + C

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

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

\int 10 cos (x) d x

\int \frac{1}{( x + 6 ) ( 36 x ^{2} + 6 x + 1 )} d x

\int (8 x^{3} - 12 x^{2} + \frac{4}{x}) d x

What is the integral of 4sec^2(4x-2) ?
The integral of 4sec^2(4x-2) is tan(4x-2)+C