What is the integral of xsqrt(5-x^2) ?

The integral of xsqrt(5-x^2) is -1/3 (5-x^2)^{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 xsqrt(5-x^2)

\int x 5 - x^{2} d x

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

Solution steps

\int x 5 - x^{2} d x

Apply u-substitution

: \int - \frac{u}{2} d u

= \int - \frac{u}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int u d u

Apply the Power Rule

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

= - \frac{1}{2} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 5 - x^{2}

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

Simplify

- \frac{1}{2} \cdot \frac{2}{3} (5 - x^{2})^{\frac{3}{2}} : - \frac{1}{3} (5 - x^{2})^{\frac{3}{2}}

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

Add a constant to the solution

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

\int e^{- s t} (3 t) d t

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

\frac{\partial}{\partial x} (ln (x^{2} + y) - z)

x \to 3 lim (x^{2} + 9)

2 sin^{2} (x)

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