en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(sqrt(x)(1-\sqrt{x))^3}

Solution

\int \frac{1}{x ( 1 - x ) ^{3}} d x

Solution

2 x + C

Solution steps

\int \frac{1}{x ( 1 - x ) ^{3}} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{x ( 1 - x ) ^{3}} = x^{- \frac{1}{2}} \frac{1}{( 1 - ) ^{3}}

= \int x^{- \frac{1}{2}} \frac{1}{( 1 ) ^{3}} d x

Simplify

x^{- \frac{1}{2}} \frac{1}{( 1 ) ^{3}} : \frac{1}{x}

= \int \frac{1}{x} d x

Apply the Power Rule

: 2 x^{\frac{1}{2}}

= 2 x^{\frac{1}{2}}

Apply radical rule:

= 2 x

Add a constant to the solution

= 2 x + C

Popular Examples

integral of 4/(5+6x)

\int \frac{4}{5 + 6 x} d x

integral of 3/((5x-2)^2)

\int \frac{3}{( 5 x - 2 ) ^{2}} d x

integral of (x^3+4)/(x(x+1))

\int \frac{x ^{3} + 4}{x ( x + 1 )} d x

integral of (x^3-3x^2+2)/(x-2)

\int \frac{x ^{3} - 3 x ^{2} + 2}{x - 2} d x

integral of 3/(t(1+t^2))

\int \frac{3}{t ( 1 + t ^{2} )} d t

Frequently Asked Questions (FAQ)

What is the integral of 1/(sqrt(x)(1-\sqrt{x))^3} ?
The integral of 1/(sqrt(x)(1-\sqrt{x))^3} is 2sqrt(x)+C