What is the integral of 22tan^{21}(x)sec^2(x) ?

The integral of 22tan^{21}(x)sec^2(x) is tan^{22}(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 22tan^{21}(x)sec^2(x)

\int 22 tan^{21} (x) sec^{2} (x) d x

tan^{22} (x) + C

Solution steps

\int 22 tan^{21} (x) sec^{2} (x) d x

Take the constant out:

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

= 22 \cdot \int tan^{21} (x) sec^{2} (x) d x

Rewrite using trig identities

= 22 \cdot \int (1 + tan^{2} (x)) tan^{21} (x) d x

Apply u-substitution

= 22 \cdot \int u^{21} d u

Apply the Power Rule

= 22 \cdot \frac{u ^{22}}{22}

Substitute back

u = tan (x)

= 22 \cdot \frac{tan ^{22} ( x )}{22}

Simplify

22 \cdot \frac{tan ^{22} ( x )}{22} : tan^{22} (x)

= tan^{22} (x)

Add a constant to the solution

= tan^{22} (x) + C

What is the integral of 22tan^{21}(x)sec^2(x) ?
The integral of 22tan^{21}(x)sec^2(x) is tan^{22}(x)+C