What is the integral of (x^2+2x+1)^5(x+1) ?

The integral of (x^2+2x+1)^5(x+1) is ((x+1)^{12})/(12)+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+2x+1)^5(x+1)

\int (x^{2} + 2 x + 1)^{5} (x + 1) d x

\frac{( x + 1 ) ^{12}}{12} + C

Solution steps

\int (x^{2} + 2 x + 1)^{5} (x + 1) d x

Apply u-substitution

= \int u^{11} d u

Apply the Power Rule

= \frac{u ^{12}}{12}

Substitute back

u = x + 1

= \frac{( x + 1 ) ^{12}}{12}

Add a constant to the solution

= \frac{( x + 1 ) ^{12}}{12} + C

\int_{- 1}^{4} 4 - x^{2} + 3 x d x

\int (\frac{1}{3}) x^{3} d x

x \to 1 lim (\frac{x + 1}{x - 1})

\int \frac{5}{2 ( 2 x - 3 ) ^{2}} d x

\frac{d}{d x} (\frac{- x ^{2} - 3}{( x ^{2} - 3 ) ^{2}})

What is the integral of (x^2+2x+1)^5(x+1) ?
The integral of (x^2+2x+1)^5(x+1) is ((x+1)^{12})/(12)+C