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

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

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

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

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

Solution steps

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

Take the constant out:

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

= \frac{1}{k !} \cdot \int x^{3 k} d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

x \to \frac{1}{5} lim (2 + ∣ 5 x - 1 ∣)

\int 2 e^{y} d y

(5 x^{2} - x + 11)^{\frac{3}{2}}

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{\frac{t}{2}}

f (x) = 3 e^{x} + 2 x, (0, 3)

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