What is the integral of \sqrt[3]{tan(x)}sec^2(x) ?

The integral of \sqrt[3]{tan(x)}sec^2(x) is 3/4 tan^{4/3}(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of \sqrt[3]{tan(x)}sec^2(x)

\int 3 tan (x) sec^{2} (x) d x

\frac{3}{4} tan^{\frac{4}{3}} (x) + C

Solution steps

\int 3 tan (x) sec^{2} (x) d x

Rewrite using trig identities

= \int (1 + tan^{2} (x)) 3 tan (x) d x

Apply u-substitution

: \int 3 u d u

= \int 3 u d u

Apply the Power Rule

: \frac{3}{4} u^{\frac{4}{3}}

= \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = tan (x)

= \frac{3}{4} tan^{\frac{4}{3}} (x)

Add a constant to the solution

= \frac{3}{4} tan^{\frac{4}{3}} (x) + C

f (x) = 800 - 800 x^{- 1}

y = \frac{2 x + 5}{x}

\int sec^{4} (x) d x

f (x) = 60 + 20 x - 4.5 x^{2}, at x = 2

- x^{2} - x + 9, - x + 7, 0

What is the integral of \sqrt[3]{tan(x)}sec^2(x) ?
The integral of \sqrt[3]{tan(x)}sec^2(x) is 3/4 tan^{4/3}(x)+C