What is the integral of (-1)^nx^{2n} ?

The integral of (-1)^nx^{2n} is ((-1)^nx^{2n+1})/(2n+1)+C

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integral of (-1)^nx^{2n}

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

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

Solution steps

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

Apply the Power Rule

: \frac{x ^{2 n + 1}}{2 n + 1}

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

Multiply fractions:

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

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

Add a constant to the solution

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

x \to 0 lim ((x - 2)^{2})

\frac{d ^{2}}{d x ^{2}} (x e^{x})

\frac{d y}{d t} + 2 y = 0

- 3 e^{- 3 x}

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

What is the integral of (-1)^nx^{2n} ?
The integral of (-1)^nx^{2n} is ((-1)^nx^{2n+1})/(2n+1)+C