What is the integral of sqrt(2t) ?

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

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integral of sqrt(2t)

\int 2 t d t

2 t t - \frac{2}{3} t^{\frac{3}{2}} + C

Solution steps

\int 2 t d t

Apply Integration By Parts

: 2 t t - \int \frac{t}{2} d t

= 2 t t - \int \frac{t}{2} d t

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

= 2 t t - \frac{2}{3} t^{\frac{3}{2}}

Add a constant to the solution

= 2 t t - \frac{2}{3} t^{\frac{3}{2}} + C

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