What is the integral of \sqrt[4]{2x+5} ?

The integral of \sqrt[4]{2x+5} is 2/5 (2x+5)^{5/4}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of \sqrt[4]{2x+5}

\frac{2}{5} (2 x + 5)^{\frac{5}{4}} + C

Solution steps

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{4}{5} u^{\frac{5}{4}}

= \frac{1}{2} \cdot \frac{4}{5} u^{\frac{5}{4}}

Substitute back

u = 2 x + 5

= \frac{1}{2} \cdot \frac{4}{5} (2 x + 5)^{\frac{5}{4}}

Simplify

\frac{1}{2} \cdot \frac{4}{5} (2 x + 5)^{\frac{5}{4}} : \frac{2}{5} (2 x + 5)^{\frac{5}{4}}

= \frac{2}{5} (2 x + 5)^{\frac{5}{4}}

Add a constant to the solution

= \frac{2}{5} (2 x + 5)^{\frac{5}{4}} + C

\frac{d}{d x} (ln (\frac{e ^{x} arcsin ( 2 x )}{x + 2}))

\frac{d}{d x} (2 e^{x} - 1)

e^{x}, e^{2 x}, 0, 1

f (x) = x^{2} (5 x - 1)^{3}

What is the integral of \sqrt[4]{2x+5} ?
The integral of \sqrt[4]{2x+5} is 2/5 (2x+5)^{5/4}+C