en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4x^3+2x+1

Solution

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

Solution

x^{4} + x^{2} + x + C

Solution steps

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

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

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

\int 1 d x = x

= x^{4} + x^{2} + x

Add a constant to the solution

= x^{4} + x^{2} + x + C

Popular Examples

integral of 5/4

\int \frac{5}{4} d x

integral of 1/a e^{-x/a}

\int \frac{1}{a} e^{- \frac{x}{a}} d x

integral of (3x^3)/(sqrt(2-9x^4))

\int \frac{3 x ^{3}}{2 - 9 x ^{4}} d x

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

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

integral of (6x)/(x^4+1)

\int \frac{6 x}{x ^{4} + 1} d x

Frequently Asked Questions (FAQ)

What is the integral of 4x^3+2x+1 ?
The integral of 4x^3+2x+1 is x^4+x^2+x+C