What is the integral of 20tan(2x)sec^2(2x) ?

The integral of 20tan(2x)sec^2(2x) is 5tan^2(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 20tan(2x)sec^2(2x)

\int 20 tan (2 x) sec^{2} (2 x) d x

5 tan^{2} (2 x) + C

Solution steps

\int 20 tan (2 x) sec^{2} (2 x) d x

Take the constant out:

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

= 20 \cdot \int tan (2 x) sec^{2} (2 x) d x

Apply u-substitution

= 20 \cdot \int \frac{u}{2} d u

Take the constant out:

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

= 20 \cdot \frac{1}{2} \cdot \int u d u

Apply the Power Rule

= 20 \cdot \frac{1}{2} \cdot \frac{u ^{2}}{2}

Substitute back

u = tan (2 x)

= 20 \cdot \frac{1}{2} \cdot \frac{tan ^{2} ( 2 x )}{2}

Simplify

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

= 5 tan^{2} (2 x)

Add a constant to the solution

= 5 tan^{2} (2 x) + C

What is the integral of 20tan(2x)sec^2(2x) ?
The integral of 20tan(2x)sec^2(2x) is 5tan^2(2x)+C