What is the integral of x^2sqrt(x^3+4) ?

The integral of x^2sqrt(x^3+4) is 2/9 (x^3+4)^{3/2}+C

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integral of x^2sqrt(x^3+4)

\int x^{2} x^{3} + 4 d x

\frac{2}{9} (x^{3} + 4)^{\frac{3}{2}} + C

Solution steps

\int x^{2} x^{3} + 4 d x

Apply u-substitution

: \int \frac{u}{3} d u

= \int \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = x^{3} + 4

= \frac{1}{3} \cdot \frac{2}{3} (x^{3} + 4)^{\frac{3}{2}}

Simplify

\frac{1}{3} \cdot \frac{2}{3} (x^{3} + 4)^{\frac{3}{2}} : \frac{2}{9} (x^{3} + 4)^{\frac{3}{2}}

= \frac{2}{9} (x^{3} + 4)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} (x^{3} + 4)^{\frac{3}{2}} + C

y^{^{'}} - 4 y = 6 e^{6 t}

\frac{d}{d x} ((c_{1} + c_{2} x) e^{- 3 x})

x \to 0 lim (\frac{( 1 + x ^{2} ) - 1}{x})

x \to \frac{π}{3} lim (sin (3 x))

n = 5 \sum \infty e^{7 - 6 n}

What is the integral of x^2sqrt(x^3+4) ?
The integral of x^2sqrt(x^3+4) is 2/9 (x^3+4)^{3/2}+C