What is the integral of sec^7(6x)tan(6x) ?

The integral of sec^7(6x)tan(6x) is 1/42 sec^7(6x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sec^7(6x)tan(6x)

\int sec^{7} (6 x) tan (6 x) d x

\frac{1}{42} sec^{7} (6 x) + C

Solution steps

\int sec^{7} (6 x) tan (6 x) d x

Apply u-substitution

: \int sec^{7} (u) tan (u) \frac{1}{6} d u

= \int sec^{7} (u) tan (u) \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int sec^{7} (u) tan (u) d u

Apply u-substitution

: \int v^{6} d v

= \frac{1}{6} \cdot \int v^{6} d v

Apply the Power Rule

: \frac{v ^{7}}{7}

= \frac{1}{6} \cdot \frac{v ^{7}}{7}

Substitute back

= \frac{1}{6} \cdot \frac{sec ^{7} ( 6 x )}{7}

Simplify

\frac{1}{6} \cdot \frac{sec ^{7} ( 6 x )}{7} : \frac{1}{42} sec^{7} (6 x)

= \frac{1}{42} sec^{7} (6 x)

Add a constant to the solution

= \frac{1}{42} sec^{7} (6 x) + C

\int sin (4 x) cos (8 x) d x

\int 4 cos (2 t) e^{t} d t

\int - 2 sin (2 π x) d x

\int \frac{1}{h - 16} d h

\int \frac{5 x ^{2}}{3 x ^{3} + 7} d x

What is the integral of sec^7(6x)tan(6x) ?
The integral of sec^7(6x)tan(6x) is 1/42 sec^7(6x)+C