What is the integral of (4sqrt(x)-4/(sqrt(x))) ?

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

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integral of (4sqrt(x)-4/(sqrt(x)))

\int (4 x - \frac{4}{x}) d x

\frac{8}{3} x^{\frac{3}{2}} - 8 x + C

Solution steps

\int 4 x - \frac{4}{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 4 x d x - \int \frac{4}{x} d x

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

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

= \frac{8}{3} x^{\frac{3}{2}} - 8 x

Add a constant to the solution

= \frac{8}{3} x^{\frac{3}{2}} - 8 x + C

x^{3} (x - 8)^{2}

y = \frac{36}{x ^{2} + 2}, (1, 12)

\frac{\partial}{\partial x} (\frac{a x - 5}{- y ^{2} + 1})

x \to 0 + lim (arctan (x))

\int \frac{x ^{4}}{4 + x ^{2}} d x

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