What is the integral of (3000)/(sqrt(200x)) ?

The integral of (3000)/(sqrt(200x)) is 300sqrt(2)sqrt(x)+C

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integral of (3000)/(sqrt(200x))

\int \frac{3000}{200 x} d x

3002 x + C

Solution steps

\int \frac{3000}{200 x} d x

Take the constant out:

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

= 3000 \cdot \int \frac{1}{200 x} d x

Apply Integration By Parts

: \frac{1}{10 2} x - \int - \frac{1}{20 2 x ^{\frac{1}{2}}} d x

= 3000 (\frac{1}{10 2} x - \int - \frac{1}{20 2 x ^{\frac{1}{2}}} d x)

\int - \frac{1}{20 2 x ^{\frac{1}{2}}} d x = - \frac{1}{10 2} x

= 3000 (\frac{1}{10 2} x - (- \frac{1}{10 2} x))

Simplify

3000 (\frac{1}{10 2} x - (- \frac{1}{10 2} x)) : 3002 x

= 3002 x

Add a constant to the solution

= 3002 x + C

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What is the integral of (3000)/(sqrt(200x)) ?
The integral of (3000)/(sqrt(200x)) is 300sqrt(2)sqrt(x)+C