What is the integral of (x^2+x+1) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2+x+1)

\int (x^{2} + x + 1) d x

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

Solution steps

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

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

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

\int 1 d x = x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

\int cos (θ) sin^{2} (θ) d θ

\frac{\partial}{\partial y} (x^{2} cos (e^{x y}))

y^{^{''}} + 6 y^{^{'}} + 9 y = - x e^{4 x}

\int \frac{8 x}{x ^{2} + x + 1} d x

x \to - 2 lim (x^{2} - 1)

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