What is the integral of (x^n)/(n!) ?

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

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integral of (x^n)/(n!)

\int \frac{x ^{n}}{n !} d x

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

Solution steps

\int \frac{x ^{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 !} \cdot \int x^{n} d x

Apply the Power Rule

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

= \frac{1}{n !} \cdot \frac{x ^{n + 1}}{n + 1}

Simplify

\frac{1}{n !} \cdot \frac{x ^{n + 1}}{n + 1} : \frac{x ^{n + 1}}{n ! ( n + 1 )}

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

Add a constant to the solution

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

\frac{d y}{d t} - \frac{y}{2 t} = 3 t

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

\frac{d}{d x} ((x^{3} - 9 x)^{- \frac{1}{3}})

\frac{d}{d x} (tan (cot (ln (x))) + sec (e^{x}))

x \to 0 + lim (\frac{sin ( x )}{x})

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