What is the integral of 1/((1+sqrt(x))^5\sqrt{x)} ?

The integral of 1/((1+sqrt(x))^5\sqrt{x)} is -1/(2(sqrt(x)+1)^4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((1+sqrt(x))^5\sqrt{x)}

\int \frac{1}{( 1 + x ) ^{5} x} d x

- \frac{1}{2 ( x + 1 ) ^{4}} + C

Solution steps

\int \frac{1}{( 1 + x ) ^{5} x} d x

Apply u-substitution

: \int \frac{2}{( 1 + u ) ^{5}} d u

= \int \frac{2}{( 1 + u ) ^{5}} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{( 1 + u ) ^{5}} d u

Apply u-substitution

: \int \frac{1}{v ^{5}} d v

= 2 \cdot \int \frac{1}{v ^{5}} d v

Apply the Power Rule

: - \frac{1}{4 v ^{4}}

= 2 (- \frac{1}{4 v ^{4}})

Substitute back

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

Simplify

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

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

Add a constant to the solution

= - \frac{1}{2 ( x + 1 ) ^{4}} + C

x \to 0 lim (\frac{sin ^{2} ( 2 x )}{x})

f (x) = tan (e^{x})

\frac{x ^{2} - 5 x}{x + 1}

n = 0 \sum \infty \frac{5 ^{n}}{n !}

\int 8 e^{- 2 x} d x

What is the integral of 1/((1+sqrt(x))^5\sqrt{x)} ?
The integral of 1/((1+sqrt(x))^5\sqrt{x)} is -1/(2(sqrt(x)+1)^4)+C