What is the integral of (5e^{ln(x^2)})/x ?

The integral of (5e^{ln(x^2)})/x is (5x^2)/2+C

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integral of (5e^{ln(x^2)})/x

\int \frac{5 e ^{l n (x^{2})}}{x} d x

\frac{5 x ^{2}}{2} + C

Solution steps

\int \frac{5 e ^{l n (x^{2})}}{x} d x

Take the constant out:

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

= 5 \cdot \int \frac{e ^{l n (x^{2})}}{x} d x

Simplify

\frac{e ^{l n (x^{2})}}{x} : x

= 5 \cdot \int x d x

Apply the Power Rule

= 5 \cdot \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{5 x ^{2}}{2}

Add a constant to the solution

= \frac{5 x ^{2}}{2} + C

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What is the integral of (5e^{ln(x^2)})/x ?
The integral of (5e^{ln(x^2)})/x is (5x^2)/2+C