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

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

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integral of 2x(sqrt(x+x))

\int 2 x (x + x) d x

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

Solution steps

\int 2 x 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 + x d x

x + x = 2 x

= 2 \cdot \int 2 x x d x

Take the constant out:

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

= 22 \cdot \int x x d x

Simplify

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

= 22 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

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

= 22 \frac{2}{5} x^{\frac{5}{2}}

Simplify

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

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

Add a constant to the solution

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

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What is the integral of 2x(sqrt(x+x)) ?
The integral of 2x(sqrt(x+x)) is (4sqrt(2))/5 x^{5/2}+C