What is the integral of (x^nn(x)) ?

The integral of (x^nn(x)) is (nx^{n+2})/(n+2)+C

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integral of (x^nn(x))

\int (x^{n} n (x)) d x

\frac{n x ^{n + 2}}{n + 2} + C

Solution steps

\int x^{n} n x d x

Take the constant out:

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

= n \cdot \int x^{n} x d x

Simplify

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

= n \cdot \int x^{n + 1} d x

Apply the Power Rule

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

= n \frac{x ^{n + 2}}{n + 2}

Multiply fractions:

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

= \frac{n x ^{n + 2}}{n + 2}

Add a constant to the solution

= \frac{n x ^{n + 2}}{n + 2} + C

t y^{^{'}} + 2 y = 4 t^{2}, y (1) = 2

\frac{ln ( 2 x + 5 )}{ln ( 3 )}

\int e^{z} cos (x) d x

f (x) = - 1 - 4 x^{2}, (3, - 37)

2 y^{^{''}} + 72 y = 0

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