What is the integral of (1000)/(sqrt(100x)) ?

The integral of (1000)/(sqrt(100x)) is 1000(1/10 sqrt(x)+1/10 sqrt(x))+C

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integral of (1000)/(sqrt(100x))

\int \frac{1000}{100 x} d x

1000 (\frac{1}{10} x + \frac{1}{10} x) + C

Solution steps

\int \frac{1000}{100 x} d x

Take the constant out:

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

= 1000 \cdot \int \frac{1}{100 x} d x

Apply Integration By Parts

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

= 1000 (\frac{1}{10} x - \int - \frac{1}{20 x ^{\frac{1}{2}}} d x)

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

= 1000 (\frac{1}{10} x - (- \frac{1}{10} x^{\frac{1}{2}}))

Simplify

1000 (\frac{1}{10} x - (- \frac{1}{10} x^{\frac{1}{2}})) : 1000 (\frac{1}{10} x + \frac{1}{10} x)

= 1000 (\frac{1}{10} x + \frac{1}{10} x)

Add a constant to the solution

= 1000 (\frac{1}{10} x + \frac{1}{10} x) + C

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What is the integral of (1000)/(sqrt(100x)) ?
The integral of (1000)/(sqrt(100x)) is 1000(1/10 sqrt(x)+1/10 sqrt(x))+C