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

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

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integral of 3sqrt(2x)

\int 3 2 x d x

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

Solution steps

\int 3 2 x d x

Take the constant out:

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

= 3 \cdot \int 2 x d x

Apply Integration By Parts

: 2 x x - \int \frac{x}{2} d x

= 3 (2 x x - \int \frac{x}{2} d x)

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

= 3 (2 x x - \frac{2}{3} x^{\frac{3}{2}})

Simplify

3 (2 x x - \frac{2}{3} x^{\frac{3}{2}}) : 32 x x - 2 x^{\frac{3}{2}}

= 32 x x - 2 x^{\frac{3}{2}}

Add a constant to the solution

= 32 x x - 2 x^{\frac{3}{2}} + C

\frac{\partial}{\partial x} (7 x sin (5 x^{2} y))

\int x x x + 1 d x

y^{^{''}} + 4 y^{^{'}} + 3 y = 15 t e^{3 t}

x^{2} = 4 y, 3 x - 4 y + 4 = 0

y^{^{'}} + y = e^{- t} sin (t), y (0) = 1

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