Evaluate the integral using the indicated trigonometric substitution. integral {x^3} / {(x^2 +...

Question:

Evaluate the integral using the indicated trigonometric substitution.

{eq}\displaystyle \int \frac {x^3} {(x^2 + 25)^{\frac 1 2}}\ dx,\ x = 5 \tan \theta {/eq}.

Integrals:

The given indefinite integral is complex to solve. As we cannot solve the given integral directly, therefore we will simplify the function by applying the substitution method. The substitution for the variable is already given to us.

Answer and Explanation: 1

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{eq}\begin{align*} & \int \frac {x^3} {(x^2 + 25)^{\frac 1 2}} \ dx \end{align*} {/eq}

Put,

{eq}\begin{align*} & x = 5 \tan \theta...

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How to Use Trigonometric Substitution to Solve Integrals

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Chapter 13 / Lesson 12
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Trigonometric 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.


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