What is the integral of (2t+6)/(sqrt(t)) ?

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

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integral of (2t+6)/(sqrt(t))

\int \frac{2 t + 6}{t} d t

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

Solution steps

\int \frac{2 t + 6}{t} d t

Apply Integration By Parts

: 2 t (2 t + 6) - \int 4 t d t

= 2 t (2 t + 6) - \int 4 t d t

\int 4 t d t = \frac{8}{3} t^{\frac{3}{2}}

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

Add a constant to the solution

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

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