What is the integral of (sqrt(x)+1/(6sqrt(x))) ?

The integral of (sqrt(x)+1/(6sqrt(x))) is 2/3 x^{3/2}+1/3 sqrt(x)+C

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integral of (sqrt(x)+1/(6sqrt(x)))

\int (x + \frac{1}{6 x}) d x

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

Solution steps

\int x + \frac{1}{6 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}{6 x} d x

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

\int \frac{1}{6 x} d x = \frac{1}{3} x

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

Add a constant to the solution

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

\int_{0}^{1} x (x^{2} - x) d x

\int \frac{x}{y} d y

n = 0 \sum \infty \frac{- 1 ^{n}}{n !}

y = x^{10} + 1 + 1 - x

\frac{d}{d x} (9 x + 4)

What is the integral of (sqrt(x)+1/(6sqrt(x))) ?
The integral of (sqrt(x)+1/(6sqrt(x))) is 2/3 x^{3/2}+1/3 sqrt(x)+C