Integrate: integral of (sqrt x)/(1 + fourth root of x) dx.

Question:

Integrate: {eq}\; \int \frac{\sqrt{x}}{1 + \sqrt[4]{x}} \, \mathrm{d}x {/eq}.

Substitution rule:

In indefinite integral, integration by substitution or u substitution plays an important role to find the integration of the given problem. In this method, we have taken one function as u and then replace the remaining function as in terms of u and then find the integration.

Answer and Explanation:

Given {eq}\; \int \frac{\sqrt{x}}{1 + \sqrt[4]{x}} \, \mathrm{d}x {/eq}.

Apply u-substitution {eq}\:u=x^{\frac{1}{4}},...

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How to Solve Integrals Using Substitution

from Math 104: Calculus

Chapter 13 / Lesson 5
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