What is the integral of (125x^9) ?

The integral of (125x^9) is (25x^{10})/2+C

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integral of (125x^9)

\int (125 x^{9}) d x

\frac{25 x ^{10}}{2} + C

Solution steps

\int 125 x^{9} d x

Take the constant out:

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

= 125 \cdot \int x^{9} d x

Apply the Power Rule

= 125 \cdot \frac{x ^{10}}{10}

Simplify

125 \cdot \frac{x ^{10}}{10} : \frac{25 x ^{10}}{2}

= \frac{25 x ^{10}}{2}

Add a constant to the solution

= \frac{25 x ^{10}}{2} + C