What is the integral of (sqrt(x)+1/(8sqrt(x))) ?

The integral of (sqrt(x)+1/(8sqrt(x))) is 2/3 x^{3/2}+1/4 sqrt(x)+C

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integral of (sqrt(x)+1/(8sqrt(x)))

\int (x + \frac{1}{8 x}) d x

\frac{2}{3} x^{\frac{3}{2}} + \frac{1}{4} x + C

Solution steps

\int x + \frac{1}{8 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}{8 x} d x

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

\int \frac{1}{8 x} d x = \frac{1}{4} x

= \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{4} x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{4} x + C

\int \frac{12}{x} d x

ln (x^{4} + x)

\frac{\partial}{\partial x} (e^{- 2 x} cos (- 3 y))

\frac{d}{d x} (arcsin (\frac{x ^{2} - 1}{x ^{2}}))

f (x) = \frac{3}{x ^{7}}

What is the integral of (sqrt(x)+1/(8sqrt(x))) ?
The integral of (sqrt(x)+1/(8sqrt(x))) is 2/3 x^{3/2}+1/4 sqrt(x)+C