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

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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

x \to 0 lim (\frac{5 x ^{n} - 3 x ^{n - 1} + 4 x ^{n - 2}}{2 x ^{n} - 6 x ^{n - 2}})

f (x) = 5 x + 3

\frac{\partial}{\partial x} (- 4 y^{4} sin (4 x))

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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