What is the integral of (-1)^nx^n ?

The integral of (-1)^nx^n is ((-1)^nx^{n+1})/(n+1)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (-1)^nx^n

\int (- 1)^{n} x^{n} d x

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

Solution steps

\int (- 1)^{n} x^{n} d x

Take the constant out:

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

= (- 1)^{n} \cdot \int x^{n} d x

Apply the Power Rule

: \frac{x ^{n + 1}}{n + 1}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

\int y^{3} (2 y^{2} - 3) d y

\frac{\partial}{\partial x} (2 y + y e^{x})

\frac{d x}{d t} = - 3 x

h \to 0 lim (\frac{e ^{2 h} - 1}{h})

\frac{d}{d x} (x \cdot cos (x))

What is the integral of (-1)^nx^n ?
The integral of (-1)^nx^n is ((-1)^nx^{n+1})/(n+1)+C