What is the integral of (e^{3ln(x)})/(\sqrt[7]{x^3)} ?

The integral of (e^{3ln(x)})/(\sqrt[7]{x^3)} is 7/25 x^{25/7}+C

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integral of (e^{3ln(x)})/(\sqrt[7]{x^3)}

\frac{7}{25} x^{\frac{25}{7}} + C

Solution steps

assuming

x \geq 0

= \int \frac{e ^{3 l n (x)}}{x ^{\frac{3}{7}}} d x

Simplify

\frac{e ^{3 l n (x)}}{x ^{\frac{3}{7}}} : x^{\frac{18}{7}}

= \int x^{\frac{18}{7}} d x

Apply the Power Rule

: \frac{7}{25} x^{\frac{25}{7}}

= \frac{7}{25} x^{\frac{25}{7}}

Add a constant to the solution

= \frac{7}{25} x^{\frac{25}{7}} + C

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What is the integral of (e^{3ln(x)})/(\sqrt[7]{x^3)} ?
The integral of (e^{3ln(x)})/(\sqrt[7]{x^3)} is 7/25 x^{25/7}+C