What is the integral of (2-x)^6 ?

The integral of (2-x)^6 is -((2-x)^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 (2-x)^6

\int (2 - x)^{6} d x

- \frac{( 2 - x ) ^{7}}{7} + C

Solution steps

\int (2 - x)^{6} d x

Apply u-substitution

: \int - u^{6} d u

= \int - u^{6} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{6} d u

Apply the Power Rule

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

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

Substitute back

u = 2 - x

= - \frac{( 2 - x ) ^{7}}{7}

Add a constant to the solution

= - \frac{( 2 - x ) ^{7}}{7} + C

\int x \frac{1}{3} d x

\int \frac{e ^{x - 1}}{x - 1} d x

\int \frac{2 x}{x ^{2} - x - 6} d x

\int 9 t e^{3 t} d t

\int \frac{2 x + 3}{x ^{2} + 3 x + 5} d x