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

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

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integral of (x^{n+1})/(n+1)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= \frac{1}{n + 1} \cdot \frac{x ^{n + 2}}{n + 2}

Simplify

\frac{1}{n + 1} \cdot \frac{x ^{n + 2}}{n + 2} : \frac{x ^{n + 2}}{( n + 1 ) ( n + 2 )}

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

Add a constant to the solution

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

\frac{d}{d x} (ln^{x} (x))

\frac{d}{d t} (\frac{1}{e ^{t}})

f (x) = \frac{1 + 3 x}{1 - 3 x}

\int_{0}^{1} [x - x^{k}] d x

\frac{d y}{d x} - \frac{y}{2} = \frac{5}{2}

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