What is the integral of 1/2 sec^2(5x) ?

The integral of 1/2 sec^2(5x) is 1/10 tan(5x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/2 sec^2(5x)

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

\frac{1}{10} tan (5 x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

Use the common integral:

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

= \frac{1}{2} \cdot \frac{1}{5} tan (u)

Substitute back

u = 5 x

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

Simplify

\frac{1}{2} \cdot \frac{1}{5} tan (5 x) : \frac{1}{10} tan (5 x)

= \frac{1}{10} tan (5 x)

Add a constant to the solution

= \frac{1}{10} tan (5 x) + C

What is the integral of 1/2 sec^2(5x) ?
The integral of 1/2 sec^2(5x) is 1/10 tan(5x)+C