What is the integral of (x^{3n})/(n!) ?

The integral of (x^{3n})/(n!) is (x^{3n+1})/(n!(3n+1))+C

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integral of (x^{3n})/(n!)

\int \frac{x ^{3 n}}{n !} d x

\frac{x ^{3 n + 1}}{n ! ( 3 n + 1 )} + C

Solution steps

\int \frac{x ^{3 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^{3 n} d x

Apply the Power Rule

: \frac{x ^{3 n + 1}}{3 n + 1}

= \frac{1}{n !} \cdot \frac{x ^{3 n + 1}}{3 n + 1}

Simplify

\frac{1}{n !} \cdot \frac{x ^{3 n + 1}}{3 n + 1} : \frac{x ^{3 n + 1}}{n ! ( 3 n + 1 )}

= \frac{x ^{3 n + 1}}{n ! ( 3 n + 1 )}

Add a constant to the solution

= \frac{x ^{3 n + 1}}{n ! ( 3 n + 1 )} + C

\frac{1}{s ^{2} + 2 s + 4}

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

f (x) = (2 x^{3} + 5)^{10}

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

\int \frac{1}{x ^{2} + d ^{2}} d x

What is the integral of (x^{3n})/(n!) ?
The integral of (x^{3n})/(n!) is (x^{3n+1})/(n!(3n+1))+C