What is the integral of sec^5(3x)tan(3x) ?

The integral of sec^5(3x)tan(3x) is 1/15 sec^5(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^5(3x)tan(3x)

\int sec^{5} (3 x) tan (3 x) d x

\frac{1}{15} sec^{5} (3 x) + C

Solution steps

\int sec^{5} (3 x) tan (3 x) d x

Apply u-substitution

: \int sec^{5} (u) tan (u) \frac{1}{3} d u

= \int sec^{5} (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^{5} (u) tan (u) d u

Apply u-substitution

: \int v^{4} d v

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

Apply the Power Rule

: \frac{v ^{5}}{5}

= \frac{1}{3} \cdot \frac{v ^{5}}{5}

Substitute back

= \frac{1}{3} \cdot \frac{sec ^{5} ( 3 x )}{5}

Simplify

\frac{1}{3} \cdot \frac{sec ^{5} ( 3 x )}{5} : \frac{1}{15} sec^{5} (3 x)

= \frac{1}{15} sec^{5} (3 x)

Add a constant to the solution

= \frac{1}{15} sec^{5} (3 x) + C

\frac{x}{y}

\int \frac{1}{( x ^{2} - 144 ) ^{\frac{3}{2}}} d x

\frac{d y}{d x} = 6 y^{\frac{2}{3}}

\int \frac{ln ( x )}{81} d x

\int x^{3} e^{- 2 x^{2}} d x

What is the integral of sec^5(3x)tan(3x) ?
The integral of sec^5(3x)tan(3x) is 1/15 sec^5(3x)+C