What is the integral of 21e^{9ln(x)} ?

The integral of 21e^{9ln(x)} is (21x^{10})/(10)+C

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integral of 21e^{9ln(x)}

\int 21 e^{9 l n (x)} d x

\frac{21 x ^{10}}{10} + C

Solution steps

\int 21 e^{9 l n (x)} d x

Take the constant out:

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

= 21 \cdot \int e^{9 l n (x)} d x

Simplify

e^{9 l n (x)} : x^{9}

= 21 \cdot \int x^{9} d x

Apply the Power Rule

: \frac{x ^{10}}{10}

= 21 \cdot \frac{x ^{10}}{10}

Multiply fractions:

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

= \frac{21 x ^{10}}{10}

Add a constant to the solution

= \frac{21 x ^{10}}{10} + C

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What is the integral of 21e^{9ln(x)} ?
The integral of 21e^{9ln(x)} is (21x^{10})/(10)+C