What is the integral of (2x^4+1)/(5x^3) ?

The integral of (2x^4+1)/(5x^3) is 1/5 (x^2-1/(2x^2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x^4+1)/(5x^3)

\int \frac{2 x ^{4} + 1}{5 x ^{3}} d x

\frac{1}{5} (x^{2} - \frac{1}{2 x ^{2}}) + C

Solution steps

\int \frac{2 x ^{4} + 1}{5 x ^{3}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int \frac{2 x ^{4} + 1}{x ^{3}} d x

Expand

\frac{2 x ^{4} + 1}{x ^{3}} : 2 x + \frac{1}{x ^{3}}

= \frac{1}{5} \cdot \int 2 x + \frac{1}{x ^{3}} 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

= \frac{1}{5} (\int 2 x d x + \int \frac{1}{x ^{3}} d x)

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

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

= \frac{1}{5} (x^{2} - \frac{1}{2 x ^{2}})

Add a constant to the solution

= \frac{1}{5} (x^{2} - \frac{1}{2 x ^{2}}) + C

\frac{d}{d x} ((x sinh (x) + cos (x))^{5})

\int x sin (\frac{1}{10}) x d x

\int_{0}^{1} 2 π (x + 9) x^{2} d x

(1 + y) d x - (1 - x) d y = 0

x \to 10 lim (\frac{x}{2})

What is the integral of (2x^4+1)/(5x^3) ?
The integral of (2x^4+1)/(5x^3) is 1/5 (x^2-1/(2x^2))+C