What is the integral of 3tan(x)sec^7(x) ?

The integral of 3tan(x)sec^7(x) is 3/7 sec^7(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 3tan(x)sec^7(x)

\int 3 tan (x) sec^{7} (x) d x

\frac{3}{7} sec^{7} (x) + C

Solution steps

\int 3 tan (x) sec^{7} (x) d x

Take the constant out:

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

= 3 \cdot \int tan (x) sec^{7} (x) d x

Apply u-substitution

= 3 \cdot \int u^{6} d u

Apply the Power Rule

= 3 \cdot \frac{u ^{7}}{7}

Substitute back

u = sec (x)

= 3 \cdot \frac{sec ^{7} ( x )}{7}

Simplify

3 \cdot \frac{sec ^{7} ( x )}{7} : \frac{3}{7} sec^{7} (x)

= \frac{3}{7} sec^{7} (x)

Add a constant to the solution

= \frac{3}{7} sec^{7} (x) + C

What is the integral of 3tan(x)sec^7(x) ?
The integral of 3tan(x)sec^7(x) is 3/7 sec^7(x)+C