What is the integral of sqrt(2x)og(2-x)x ?

The integral of sqrt(2x)og(2-x)x is og((4sqrt(2))/5 x^{5/2}-sqrt(2) 2/7 x^{7/2})+C

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integral of sqrt(2x)og(2-x)x

\int 2 x o g (2 - x) x

o g (\frac{4 2}{5} x^{\frac{5}{2}} - 2 \frac{2}{7} x^{\frac{7}{2}}) + C

Solution steps

\int 2 x o g (2 - x) x d x

Take the constant out:

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

= o g \cdot \int (2 - x) 2 x x d x

Expand

(2 - x) 2 x x : 2^{\frac{3}{2}} x^{\frac{3}{2}} - 2 x^{\frac{5}{2}}

= o g \cdot \int 2^{\frac{3}{2}} x^{\frac{3}{2}} - 2 x^{\frac{5}{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= o g (\int 2^{\frac{3}{2}} x^{\frac{3}{2}} d x - \int 2 x^{\frac{5}{2}} d x)

\int 2^{\frac{3}{2}} x^{\frac{3}{2}} d x = \frac{4 2}{5} x^{\frac{5}{2}}

\int 2 x^{\frac{5}{2}} d x = 2 \frac{2}{7} x^{\frac{7}{2}}

= o g (\frac{4 2}{5} x^{\frac{5}{2}} - 2 \frac{2}{7} x^{\frac{7}{2}})

Add a constant to the solution

= o g (\frac{4 2}{5} x^{\frac{5}{2}} - 2 \frac{2}{7} x^{\frac{7}{2}}) + C

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What is the integral of sqrt(2x)og(2-x)x ?
The integral of sqrt(2x)og(2-x)x is og((4sqrt(2))/5 x^{5/2}-sqrt(2) 2/7 x^{7/2})+C