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

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

t \frac{d y}{d t} + 5 y = t

\int \frac{3 x - 1}{( 3 x ^{2} - 2 x + 1 ) ^{4}} d x

\frac{d}{d x} (\frac{I n x + 1}{I n x - 1})

\int_{0}^{1} \frac{1}{2} e^{- 2 x} 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