What is the integral of sec^5(2/3)θtan(2/3)θ ?

The integral of sec^5(2/3)θtan(2/3)θ is (sec^5(2/3))/3 tan(2/3)θ^3+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(2/3)θtan(2/3)θ

\int sec^{5} (\frac{2}{3}) θ tan (\frac{2}{3}) θ d θ

\frac{sec ^{5} ( \frac{2}{3} )}{3} tan (\frac{2}{3}) θ^{3} + C

Solution steps

\int sec^{5} (\frac{2}{3}) θ tan (\frac{2}{3}) θ d θ

Take the constant out:

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

= sec^{5} (\frac{2}{3}) tan (\frac{2}{3}) \cdot \int θθ d θ

Simplify

θθ : θ^{2}

= sec^{5} (\frac{2}{3}) tan (\frac{2}{3}) \cdot \int θ^{2} d θ

Apply the Power Rule

: \frac{θ ^{3}}{3}

= sec^{5} (\frac{2}{3}) tan (\frac{2}{3}) \frac{θ ^{3}}{3}

Simplify

sec^{5} (\frac{2}{3}) tan (\frac{2}{3}) \frac{θ ^{3}}{3} : \frac{sec ^{5} ( \frac{2}{3} )}{3} tan (\frac{2}{3}) θ^{3}

= \frac{sec ^{5} ( \frac{2}{3} )}{3} tan (\frac{2}{3}) θ^{3}

Add a constant to the solution

= \frac{sec ^{5} ( \frac{2}{3} )}{3} tan (\frac{2}{3}) θ^{3} + C

\int cos (x) sec (s - π) d s

\int cos^{2} (2 x) sin^{4} (2 x) d x

\int sin (2 x) d x

\int \frac{1}{p ( 1 - p )} d p

\int \frac{x}{x + 4} d x

What is the integral of sec^5(2/3)θtan(2/3)θ ?
The integral of sec^5(2/3)θtan(2/3)θ is (sec^5(2/3))/3 tan(2/3)θ^3+C