What is the integral of 4e^{3ln(x)} ?

The integral of 4e^{3ln(x)} is x^4+C

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integral of 4e^{3ln(x)}

\int 4 e^{3 l n (x)} d x

x^{4} + C

Solution steps

\int 4 e^{3 l n (x)} d x

Take the constant out:

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

= 4 \cdot \int e^{3 l n (x)} d x

Simplify

e^{3 l n (x)} : x^{3}

= 4 \cdot \int x^{3} d x

Apply the Power Rule

= 4 \cdot \frac{x ^{4}}{4}

Simplify

4 \cdot \frac{x ^{4}}{4} : x^{4}

= x^{4}

Add a constant to the solution

= x^{4} + C