What is the integral of 4e^{3ln(x^2)} ?

The integral of 4e^{3ln(x^2)} is (4x^7)/7+C

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integral of 4e^{3ln(x^2)}

\int 4 e^{3 l n (x^{2})} d x

\frac{4 x ^{7}}{7} + C

Solution steps

\int 4 e^{3 l n (x^{2})} 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^{2})} d x

Simplify

e^{3 l n (x^{2})} : x^{6}

= 4 \cdot \int x^{6} d x

Apply the Power Rule

= 4 \cdot \frac{x ^{7}}{7}

Multiply fractions:

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

= \frac{4 x ^{7}}{7}

Add a constant to the solution

= \frac{4 x ^{7}}{7} + C

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What is the integral of 4e^{3ln(x^2)} ?
The integral of 4e^{3ln(x^2)} is (4x^7)/7+C