en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 8x^3+1/x

Solution

\int 8 x^{3} + \frac{1}{x} d x

Solution

2 x^{4} + ln ∣ x ∣ + C

Solution steps

\int 8 x^{3} + \frac{1}{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 8 x^{3} d x + \int \frac{1}{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 x^{4} + ln ∣ x ∣

Add a constant to the solution

= 2 x^{4} + ln ∣ x ∣ + C

Popular Examples

(\partial)/(\partial y)(e^{7xe^y})

\frac{\partial}{\partial y} (e^{7 x e^{y}})

derivative of f(x)=6x^3cot(x)derivative of

f (x) = 6 x^{3} cot (x)

tangent of f(x)=x^3sqrt(5-x^2),\at x=2 tangent of

f (x) = x^{3} 5 - x^{2}, at x = 2

derivative of-1/2 e^{-x^2}

\frac{d}{d x} (- \frac{1}{2} e^{- x^{2}})

(\partial)/(\partial x)(sqrt(x^3+sin(3y)))

\frac{\partial}{\partial x} (x^{3} + sin (3 y))

Frequently Asked Questions (FAQ)

What is the integral of 8x^3+1/x ?
The integral of 8x^3+1/x is 2x^4+ln|x|+C