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

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

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

\frac{2}{5} (x + 1)^{\frac{5}{2}} + C

Solution steps

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

Apply u-substitution

: \int u^{\frac{3}{2}} d u

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

Apply the Power Rule

: \frac{2}{5} u^{\frac{5}{2}}

= \frac{2}{5} u^{\frac{5}{2}}

Substitute back

u = x + 1

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

Add a constant to the solution

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

\frac{d}{d x} (e^{t a n^{2} (x)})

\frac{\partial}{\partial x} (x + 9 y + 8 z)

\frac{d}{d x} (\frac{7}{3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9})

y = \frac{1}{x + 2}, at x = 7

x \to 8 lim (9 x + ∣ x - 8 ∣)

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