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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x+1)(x^2+x+1)^3

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

\frac{( x ^{2} + x + 1 ) ^{4}}{4} + C

Solution steps

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

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = x^{2} + x + 1

= \frac{( x ^{2} + x + 1 ) ^{4}}{4}

Add a constant to the solution

= \frac{( x ^{2} + x + 1 ) ^{4}}{4} + C

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

\int 36 e^{6 x} 5 + e^{6 x} d x

\int \frac{ln ( x ^{24} )}{x} d x

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

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