What is the integral of ((7x^3-8sqrt(x)))/x ?

The integral of ((7x^3-8sqrt(x)))/x is (7x^3)/3-16sqrt(x)+C

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integral of ((7x^3-8sqrt(x)))/x

\int \frac{( 7 x ^{3} - 8 x )}{x} d x

\frac{7 x ^{3}}{3} - 16 x + C

Solution steps

\int \frac{7 x ^{3} - 8 x}{x} d x

Expand

\frac{7 x ^{3} - 8 x}{x} : 7 x^{2} - \frac{8}{x}

= \int 7 x^{2} - \frac{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 7 x^{2} d x - \int \frac{8}{x} d x

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

\int \frac{8}{x} d x = 16 x

= \frac{7 x ^{3}}{3} - 16 x

Add a constant to the solution

= \frac{7 x ^{3}}{3} - 16 x + C

\frac{d}{d x} (\frac{5 x ^{2} + 4}{x + 3})

x \to - 1 lim (\frac{( 1 - x )}{x + 1})

y = 3 6 x^{2} + 1

- 3^{- 2} (tan (7 t))^{5}

x \to 3 lim (\frac{\frac{x}{3} + 2}{x + 1})

What is the integral of ((7x^3-8sqrt(x)))/x ?
The integral of ((7x^3-8sqrt(x)))/x is (7x^3)/3-16sqrt(x)+C