What is the integral of (6sqrt(x)) ?

The integral of (6sqrt(x)) is 4x^{3/2}+C

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integral of (6sqrt(x))

\int (6 x) d x

4 x^{\frac{3}{2}} + C

Solution steps

\int 6 x d x

Take the constant out:

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

= 6 \cdot \int x d x

Apply the Power Rule

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

= 6 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

6 \cdot \frac{2}{3} x^{\frac{3}{2}} : 4 x^{\frac{3}{2}}

= 4 x^{\frac{3}{2}}

Add a constant to the solution

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

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

1 - t

\int_{0}^{1} \frac{3 t ^{2}}{1 + t ^{3}} d t

x \to 0 lim (e^{- 2 x})

cos (\frac{x}{3})