What is the integral of (sqrt(x)+1/(5sqrt(x))) ?

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

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integral of (sqrt(x)+1/(5sqrt(x)))

\int (x + \frac{1}{5 x}) d x

\frac{2}{3} x^{\frac{3}{2}} + \frac{2}{5} x + C

Solution steps

\int x + \frac{1}{5 x} d x

Apply the Sum Rule:

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

= \int x d x + \int \frac{1}{5 x} d x

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

\int \frac{1}{5 x} d x = \frac{2}{5} x

= \frac{2}{3} x^{\frac{3}{2}} + \frac{2}{5} x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{2}{5} x + C

y = \frac{1}{12 x ^{2}}, y = x, y = \frac{x}{18}

\int \frac{3 x ^{5} - 6 x ^{2} + 2 x - 5}{x ^{3}} d x

n = 0 \sum \infty e^{4 n}

\int_{2}^{- 1} 3^{x} d x

n = 2 \sum \infty \frac{1}{n ^{\frac{3}{2}}}

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