What is the integral of 4sqrt(u) ?

The integral of 4sqrt(u) is 8/3 u^{3/2}+C

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integral of 4sqrt(u)

\int 4 u d u

\frac{8}{3} u^{\frac{3}{2}} + C

Solution steps

\int 4 u d u

Take the constant out:

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

= 4 \cdot \int u d u

Apply the Power Rule

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

= 4 \cdot \frac{2}{3} u^{\frac{3}{2}}

Simplify

4 \cdot \frac{2}{3} u^{\frac{3}{2}} : \frac{8}{3} u^{\frac{3}{2}}

= \frac{8}{3} u^{\frac{3}{2}}

Add a constant to the solution

= \frac{8}{3} u^{\frac{3}{2}} + C

y = x^{3} - 4 x^{2}, y = 2 x^{2} - 8 x

f (x) = \frac{1}{35} x^{5} + \frac{1}{4} x^{4} + x + 1

\int_{1}^{2} \frac{1}{x - 2} d x

\frac{d}{d x} (\frac{x ^{2} + 9}{x})

\frac{d}{d x} (x^{2} ln^{2} (x))