Perform the indicated integral by using trig-substitution.
{eq}\int \frac{x}{\sqrt{x^2+4}}dx {/eq}
Question:
Perform the indicated integral by using trig-substitution.
{eq}\int \frac{x}{\sqrt{x^2+4}}dx {/eq}
Integration using Trigonometric Substitution:
In this problem we are to solve the integral using trigonometric substitution. Since the integral is in the form of {eq}\sqrt{u^2+a^2} {/eq} we then use {eq}u = a\;tanz {/eq}.
Answer and Explanation: 1
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View this answerLet {eq}x = 2\;tanz {/eq}, so {eq}dx = 2\;sec^2z\;dz {/eq}:
{eq}\displaystyle \int \frac{2\;tanz}{\sqrt{4\;tan^2z + 4}}(2\;sec^2z\;dz)...
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Chapter 13 / Lesson 12Trigonometric substitutions can be useful by plugging in a function of a variable, thus simplifying the calculation of an integral. Learn how to solve integrals using substitution, tables, by parts, and Riemann Sums through a variety of examples.