What is the integral of sec^2(5x-2) ?

The integral of sec^2(5x-2) is 1/5 tan(5x-2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sec^2(5x-2)

\int sec^{2} (5 x - 2) d x

\frac{1}{5} tan (5 x - 2) + C

Solution steps

\int sec^{2} (5 x - 2) d x

Apply u-substitution

: \int sec^{2} (u) \frac{1}{5} d u

= \int sec^{2} (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= \frac{1}{5} tan (u)

Substitute back

u = 5 x - 2

= \frac{1}{5} tan (5 x - 2)

Add a constant to the solution

= \frac{1}{5} tan (5 x - 2) + C

\int 6 x - 6 d x

\int (4 - 3 x)^{8} d x

\int e^{c o s (23 t)} sin (23 t) d t

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

\int \frac{1}{u ^{2} - 10 u + 25} d u

What is the integral of sec^2(5x-2) ?
The integral of sec^2(5x-2) is 1/5 tan(5x-2)+C