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

The integral of (x+3)sqrt(x-1) is 2/5 (x-1)^{5/2}+8/3 (x-1)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+3)sqrt(x-1)

\int (x + 3) x - 1 d x

\frac{2}{5} (x - 1)^{\frac{5}{2}} + \frac{8}{3} (x - 1)^{\frac{3}{2}} + C

Solution steps

\int (x + 3) x - 1 d x

Apply u-substitution

: \int u (u + 4) d u

= \int u (u + 4) d u

Expand

u (u + 4) : u^{\frac{3}{2}} + 4 u

= \int u^{\frac{3}{2}} + 4 u d u

Apply the Sum Rule:

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

= \int u^{\frac{3}{2}} d u + \int 4 u d u

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

\int 4 u d u = \frac{8}{3} u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} + \frac{8}{3} u^{\frac{3}{2}}

Substitute back

u = x - 1

= \frac{2}{5} (x - 1)^{\frac{5}{2}} + \frac{8}{3} (x - 1)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{5} (x - 1)^{\frac{5}{2}} + \frac{8}{3} (x - 1)^{\frac{3}{2}} + C

\int \frac{( x ^{9} )}{1 + x ^{20}} d x

x e^{x}

\int x^{3} x^{2} + 28 d x

\int 2 x cos (4 x) d x

What is the integral of (x+3)sqrt(x-1) ?
The integral of (x+3)sqrt(x-1) is 2/5 (x-1)^{5/2}+8/3 (x-1)^{3/2}+C