What is the integral of (v^{3/2}+1/(v^{3/2)}) ?

The integral of (v^{3/2}+1/(v^{3/2)}) is 2/5 v^{5/2}-2/(v^{1/2)}+C

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integral of (v^{3/2}+1/(v^{3/2)})

\int (v^{\frac{3}{2}} + \frac{1}{v ^{\frac{3}{2}}}) d v

\frac{2}{5} v^{\frac{5}{2}} - \frac{2}{v ^{\frac{1}{2}}} + C

Solution steps

\int v^{\frac{3}{2}} + \frac{1}{v ^{\frac{3}{2}}} d v

Apply the Sum Rule:

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

= \int v^{\frac{3}{2}} d v + \int \frac{1}{v ^{\frac{3}{2}}} d v

\int v^{\frac{3}{2}} d v = \frac{2}{5} v^{\frac{5}{2}}

\int \frac{1}{v ^{\frac{3}{2}}} d v = - \frac{2}{v ^{\frac{1}{2}}}

= \frac{2}{5} v^{\frac{5}{2}} - \frac{2}{v ^{\frac{1}{2}}}

Add a constant to the solution

= \frac{2}{5} v^{\frac{5}{2}} - \frac{2}{v ^{\frac{1}{2}}} + C

\int_{1}^{4} (\frac{x}{2} - \frac{5}{x}) d x

x \to \frac{7}{8} lim (x^{4})

\frac{d}{d x} (\frac{e ^{x - 2}}{x})

\int \frac{2 x}{9 - 4 x ^{2}} d x

\frac{d}{d x} (2 - 2 sin (x))

What is the integral of (v^{3/2}+1/(v^{3/2)}) ?
The integral of (v^{3/2}+1/(v^{3/2)}) is 2/5 v^{5/2}-2/(v^{1/2)}+C