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

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

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

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

Solution steps

\int sec^{2} (5 x) 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

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

Add a constant to the solution

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

y = e^{10 - 7 x}

\frac{\partial}{\partial x} (2 x e^{x y^{3}})

36 - y^{2}

y^{^{''}} - 5 y^{^{'}} + 6 y = cos (2 x) + 1

x \to + (- 1) - lim (2)