What is the integral of (2000)/(sqrt(400q)) ?

The integral of (2000)/(sqrt(400q)) is 2000(1/20 sqrt(q)+1/20 sqrt(q))+C

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integral of (2000)/(sqrt(400q))

\int \frac{2000}{400 q} d q

2000 (\frac{1}{20} q + \frac{1}{20} q) + C

Solution steps

\int \frac{2000}{400 q} d q

Take the constant out:

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

= 2000 \cdot \int \frac{1}{400 q} d q

Apply Integration By Parts

: \frac{1}{20} q - \int - \frac{1}{40 q ^{\frac{1}{2}}} d q

= 2000 (\frac{1}{20} q - \int - \frac{1}{40 q ^{\frac{1}{2}}} d q)

\int - \frac{1}{40 q ^{\frac{1}{2}}} d q = - \frac{1}{20} q^{\frac{1}{2}}

= 2000 (\frac{1}{20} q - (- \frac{1}{20} q^{\frac{1}{2}}))

Simplify

2000 (\frac{1}{20} q - (- \frac{1}{20} q^{\frac{1}{2}})) : 2000 (\frac{1}{20} q + \frac{1}{20} q)

= 2000 (\frac{1}{20} q + \frac{1}{20} q)

Add a constant to the solution

= 2000 (\frac{1}{20} q + \frac{1}{20} q) + C

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What is the integral of (2000)/(sqrt(400q)) ?
The integral of (2000)/(sqrt(400q)) is 2000(1/20 sqrt(q)+1/20 sqrt(q))+C