What is the integral of sec^4(3x)tan(3x) ?

The integral of sec^4(3x)tan(3x) is 1/12 sec^4(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sec^4(3x)tan(3x)

\int sec^{4} (3 x) tan (3 x) d x

\frac{1}{12} sec^{4} (3 x) + C

Solution steps

\int sec^{4} (3 x) tan (3 x) d x

Apply u-substitution

: \int sec^{4} (u) tan (u) \frac{1}{3} d u

= \int sec^{4} (u) tan (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int sec^{4} (u) tan (u) d u

Apply u-substitution

: \int v^{3} d v

= \frac{1}{3} \cdot \int v^{3} d v

Apply the Power Rule

: \frac{v ^{4}}{4}

= \frac{1}{3} \cdot \frac{v ^{4}}{4}

Substitute back

= \frac{1}{3} \cdot \frac{sec ^{4} ( 3 x )}{4}

Simplify

\frac{1}{3} \cdot \frac{sec ^{4} ( 3 x )}{4} : \frac{1}{12} sec^{4} (3 x)

= \frac{1}{12} sec^{4} (3 x)

Add a constant to the solution

= \frac{1}{12} sec^{4} (3 x) + C

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

x \to 0 lim (\frac{e x - 1}{x})

f (x) = 4 (4 t - 1)^{2}

\int_{- \infty}^{0} x e^{- 7 x} d x

f (x) = 2 x ln (x)

What is the integral of sec^4(3x)tan(3x) ?
The integral of sec^4(3x)tan(3x) is 1/12 sec^4(3x)+C