What is the integral of (sqrt(t)-1/(sqrt(t))) ?

The integral of (sqrt(t)-1/(sqrt(t))) is 2/3 t^{3/2}-2sqrt(t)+C

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integral of (sqrt(t)-1/(sqrt(t)))

\int (t - \frac{1}{t}) d t

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

Solution steps

\int t - \frac{1}{t} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t d t - \int \frac{1}{t} d t

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

\int \frac{1}{t} d t = 2 t

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

Add a constant to the solution

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

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What is the integral of (sqrt(t)-1/(sqrt(t))) ?
The integral of (sqrt(t)-1/(sqrt(t))) is 2/3 t^{3/2}-2sqrt(t)+C