What is the integral of (4+6u)/(sqrt(u)) ?

The integral of (4+6u)/(sqrt(u)) is 2sqrt(u)(4+6u)-8u^{3/2}+C

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integral of (4+6u)/(sqrt(u))

\int \frac{4 + 6 u}{u} d u

2 u (4 + 6 u) - 8 u^{\frac{3}{2}} + C

Solution steps

\int \frac{4 + 6 u}{u} d u

Apply Integration By Parts

: 2 u (4 + 6 u) - \int 12 u d u

= 2 u (4 + 6 u) - \int 12 u d u

\int 12 u d u = 8 u^{\frac{3}{2}}

= 2 u (4 + 6 u) - 8 u^{\frac{3}{2}}

Add a constant to the solution

= 2 u (4 + 6 u) - 8 u^{\frac{3}{2}} + C

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What is the integral of (4+6u)/(sqrt(u)) ?
The integral of (4+6u)/(sqrt(u)) is 2sqrt(u)(4+6u)-8u^{3/2}+C