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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

tan^{2} (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u d u

= 2 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

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

Substitute back

u = tan (x)

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

Simplify

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

= tan^{2} (x)

Add a constant to the solution

= tan^{2} (x) + C

t^{3} e^{- 2 t}

\frac{d}{d x} (x \cdot e^{- \frac{1}{x ^{2}}})

(e^{- 5 x})^{^{'}}

\int \frac{x + 4}{x} d x

\frac{d}{d x} (a x^{3} ln (\frac{x}{4}) + b x^{2} (x - 4))

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