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

The integral of xsqrt(x^2+2) is 1/3 (x^2+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(x^2+2)

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

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

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

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

= \frac{u ^{3}}{3}

Substitute back

u = x^{2} + 2

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

Simplify

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

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

Add a constant to the solution

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

f (x) = - x^{3} + 3 x^{2}

f (x) = \frac{4}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (6 x - 9)

y^{^{'''}} - 9 y^{^{''}} + 20 y^{^{'}} = 0

\frac{\partial}{\partial x} (\frac{( x + y )}{x y - 1})

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