What is the integral of 2xsqrt(x) ?

The integral of 2xsqrt(x) is 4/5 x^{5/2}+C

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integral of 2xsqrt(x)

\int 2 x x d x

\frac{4}{5} x^{\frac{5}{2}} + C

Solution steps

\int 2 x x d x

Take the constant out:

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

= 2 \cdot \int x x d x

Simplify

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

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

Apply the Power Rule

: \frac{2}{5} x^{\frac{5}{2}}

= 2 \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

2 \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{4}{5} x^{\frac{5}{2}}

= \frac{4}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{2}} + C

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

- y^{^{'}} - 5 y = - t

\frac{d y}{d x} + 10 (tan (10 x)) y = cos (10 x)

\frac{d y}{d x} = 4 x^{3} y

\int \frac{D ( 5 x ^{2} + 5 y ^{2} ) - 1}{2} d A