Solve this integral exercise 12:30l LTEDone Ejercicio extra, valor 2 puntos sep...x4 + x6 dx

Answered: x4 + x6 dx

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.3: Quadratic Equations

Problem 51E

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Solve this integral exercise

12:30
l LTE
Done Ejercicio extra, valor 2 puntos sep...
x4 + x6 dx

Expert Solution

Step 1

Concept:

The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.

Step 2

Given:

$\int \sqrt{x^{4} + x^{6}} d x$

The objective is to integrate the given

Step 3

$\int \sqrt{x^{4} + x^{6}} d x$

On simplifying as follows,

$\int \sqrt{x^{4} + x^{6}} d x = \int x^{2} \sqrt{1 + x^{2}} d x On applying Trig substitution x=tan(u) \int \sqrt{x^{4} + x^{6}} d x = \int s e c^{3} (u) \tan^{2} (u) d u On rewriting the trignometric indentities, \int \sqrt{x^{4} + x^{6}} d x = \int s e c^{3} (u) (- 1 + s e c^{2} (u)) d u$

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