What is the integral of (10x)^n ?

The integral of (10x)^n is (10^nx^{n+1})/(n+1)+C

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integral of (10x)^n

\int (10 x)^{n} d x

\frac{1 0 ^{n} x ^{n + 1}}{n + 1} + C

Solution steps

\int (10 x)^{n} d x

Simplify

(10 x)^{n} : 1 0^{n} x^{n}

= \int 1 0^{n} x^{n} d x

Take the constant out:

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

= 1 0^{n} \cdot \int x^{n} d x

Apply the Power Rule

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

= 1 0^{n} \cdot \frac{x ^{n + 1}}{n + 1}

Multiply fractions:

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

= \frac{1 0 ^{n} x ^{n + 1}}{n + 1}

Add a constant to the solution

= \frac{1 0 ^{n} x ^{n + 1}}{n + 1} + C

\int_{2}^{5} 2 x^{3} d x

\frac{d y}{d x} = - y^{3}

y = x^{2} - 8 x + 9, (1, 2)

\frac{d}{d x} (u e^{- x})

\int 361 - x^{2} d x

What is the integral of (10x)^n ?
The integral of (10x)^n is (10^nx^{n+1})/(n+1)+C