What is the integral of (1+sqrt(x))^3 ?

The integral of (1+sqrt(x))^3 is x+2x^{3/2}+(3x^2)/2+2/5 x^{5/2}+C

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))^3

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

x + 2 x^{\frac{3}{2}} + \frac{3 x ^{2}}{2} + \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

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

Expand

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

= \int 1 + 3 x + 3 x + x^{\frac{3}{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int 3 x d x + \int 3 x d x + \int x^{\frac{3}{2}} d x

\int 1 d x = x

\int 3 x d x = 2 x^{\frac{3}{2}}

\int 3 x d x = \frac{3 x ^{2}}{2}

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

= x + 2 x^{\frac{3}{2}} + \frac{3 x ^{2}}{2} + \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= x + 2 x^{\frac{3}{2}} + \frac{3 x ^{2}}{2} + \frac{2}{5} x^{\frac{5}{2}} + C

\int_{0}^{5} \frac{5 - x}{5} d x

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

f (x) = \frac{x cos ( x ) + π}{x - π}

\int 6 tan^{3} (2 x) sec^{5} (2 x) d x

\int \frac{1}{5 + 3 x} d x

What is the integral of (1+sqrt(x))^3 ?
The integral of (1+sqrt(x))^3 is x+2x^{3/2}+(3x^2)/2+2/5 x^{5/2}+C