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

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

Popular >

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

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

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

Solution steps

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

Take the constant out:

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

= \frac{( - 1 ) ^{n}}{n !} \cdot \int x^{2 n} d x

Apply the Power Rule

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

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

Add a constant to the solution

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

\int x e^{x^{2}} d x

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

f (x) = 5 x + 30, at x = - 1

x \to - 1 + lim (∣ x ∣ - 3)

\int_{- 1}^{1} (x^{100}) d x

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