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

The integral of (x-3)(sqrt(x+3)) is 2/3 x(x+3)^{3/2}-2(x+3)^{3/2}-4/15 (x+3)^{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-3)(sqrt(x+3))

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

\frac{2}{3} x (x + 3)^{\frac{3}{2}} - 2 (x + 3)^{\frac{3}{2}} - \frac{4}{15} (x + 3)^{\frac{5}{2}} + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2}{3} (x + 3)^{\frac{3}{2}} d x = \frac{4}{15} (x + 3)^{\frac{5}{2}}

= \frac{2}{3} x (x + 3)^{\frac{3}{2}} - 2 (x + 3)^{\frac{3}{2}} - \frac{4}{15} (x + 3)^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{3} x (x + 3)^{\frac{3}{2}} - 2 (x + 3)^{\frac{3}{2}} - \frac{4}{15} (x + 3)^{\frac{5}{2}} + C

\frac{d y}{d x} - \frac{1 y}{x} = 1 - \frac{1}{x}

e^{- 3 x} - 3 e^{- 3 x} x

\int 12 x ln (7 x) d x

\frac{d}{d x} ((a^{2} + x^{2}) e^{- x^{2} - a^{2}})

\frac{d}{d x} (- 4 cos^{3} (x))

What is the integral of (x-3)(sqrt(x+3)) ?
The integral of (x-3)(sqrt(x+3)) is 2/3 x(x+3)^{3/2}-2(x+3)^{3/2}-4/15 (x+3)^{5/2}+C