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{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}{d x} (\frac{x ^{2} + 4 x + 5 x ^{3}}{x + 1})

\int_{1}^{2} 2^{- x} d x

\int_{0}^{1} \frac{25}{4 y - 1} d y

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

\frac{d P}{d x} = P - P^{2}

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