What is the integral of ((x^2))/(sqrt(5+2x^3)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((x^2))/(sqrt(5+2x^3))

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

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

Solution steps

\int \frac{x ^{2}}{5 + 2 x ^{3}} d x

Apply u-substitution

: \int \frac{1}{6 u} d u

= \int \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= \frac{1}{6} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 5 + 2 x^{3}

= \frac{1}{6} \cdot 2 (5 + 2 x^{3})^{\frac{1}{2}}

Simplify

\frac{1}{6} \cdot 2 (5 + 2 x^{3})^{\frac{1}{2}} : \frac{1}{3} 5 + 2 x^{3}

= \frac{1}{3} 5 + 2 x^{3}

Add a constant to the solution

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

\int \frac{b}{b ^{2} - 2 b + 2}

\int 3 x^{2} (x^{3} + 8)^{5} d x

y = - 2 sin (x^{2})

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

\int e^{6 t} cos (2 t) d t

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