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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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}}

Add a constant to the solution

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

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