What is the integral of (3sqrt(x)) ?

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

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integral of (3sqrt(x))

\int (3 x) d x

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

Solution steps

\int 3 x d x

Take the constant out:

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

= 3 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\int_{0}^{1} arcsin (y) d y

f (x) = x^{4} - 25 x^{2} + 144, at x = - 1

e^{\frac{x}{5}}

14 e^{x^{2}} x

\frac{\partial}{\partial x} (ln (x^{2} + 2 y^{2}))