What is the integral of (4x^3-3sqrt(x))/x ?

The integral of (4x^3-3sqrt(x))/x is (4x^3)/3-6sqrt(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4x^3-3sqrt(x))/x

\int \frac{4 x ^{3} - 3 x}{x} d x

\frac{4 x ^{3}}{3} - 6 x + C

Solution steps

\int \frac{4 x ^{3} - 3 x}{x} d x

Expand

\frac{4 x ^{3} - 3 x}{x} : 4 x^{2} - \frac{3}{x}

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

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

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

= \frac{4 x ^{3}}{3} - 6 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} - 6 x + C

y^{2} y^{^{'}} = y^{3} - 3 x

\int x (3 sec^{2} (x) - 2 tan^{2} (x)) d x

y = 3 x^{2} - 5 x

\frac{\partial}{\partial x} (2 x + 2 y + z)

\frac{d}{d x} (x^{3} y^{4})

What is the integral of (4x^3-3sqrt(x))/x ?
The integral of (4x^3-3sqrt(x))/x is (4x^3)/3-6sqrt(x)+C