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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x+1)*(x^2+x+1)

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

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

Solution steps

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

Apply u-substitution

= \int u d u

Apply the Power Rule

= \frac{u ^{2}}{2}

Substitute back

u = x^{2} + x + 1

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

Add a constant to the solution

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

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