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

The integral of (x^2-2x+1)^3 is ((x-1)^7)/7+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)^3

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

\frac{( x - 1 ) ^{7}}{7} + C

Solution steps

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

Complete the square

x^{2} - 2 x + 1 : (x - 1)^{2}

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

Apply u-substitution

: \int u^{6} d u

= \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= \frac{u ^{7}}{7}

Substitute back

u = x - 1

= \frac{( x - 1 ) ^{7}}{7}

Add a constant to the solution

= \frac{( x - 1 ) ^{7}}{7} + C

\int t sin (t) d t

7 sin (4 (t + 2)) + 3 cos (4 t - 2)

\frac{d}{d x} (ln (\frac{5 x + 3}{5 x - 3}))

\int 2 cot (2 x) d x

\int_{0}^{4 π} 5 + t^{2} d t

What is the integral of (x^2-2x+1)^3 ?
The integral of (x^2-2x+1)^3 is ((x-1)^7)/7+C